It was the decade of civil rights, the Beatles and Mao's Little Red Book. But the hand of modernity was not upon everything. It was in that same decade that Basil Hume, at the age of 37, went to a service in a non-Catholic church for the first time. Such was the climate of relations between Roman Catholic and Protestant denominations that Vatican rules meant that the man who was three years later to become abbot of the Benedictine monastery at Ampleforth was forbidden even from joining in the words of the Lord's Prayer. It was the funeral of his father, and he stood in dumb grief as the familiar words echoed around his ears.

The life of George Basil Hume, Cardinal Archbishop of Westminster who died last week, is an index to the great shift that has taken place within Britain's Catholic community during the past two generations. When Hume stood behind his father's coffin Catholicism was still in the ghetto. It was a discrete culture within a strong, but marginalised, community which existed on the periphery of British society - a curious hybrid of Brideshead recusant aristocracy and Irish peasant piety. It was dominated by the dark suspicion which surrounded Rome in the English imagination. Roman Catholics were seen to owe allegiance to a foreign power, and the notion of English Catholicism seemed as unnatural as the "mixed marriage", as the phrase of the time had it, between Hume's Scottish Protestant father and French Catholic mother.

The marginalisation had not been solely down to the Pope's autocratic dogmatism on where and how his flock might pray. There was a matching resistance among the English Establishment: when a previous cardinal had tried to present a Loyal Address on behalf of the Catholic bishops, clergy and laity to King George V, it was returned with a tart message from a junior Home Office official to the effect that it was "not appropriate".

It was not just the character of Cardinal Hume that altered this. By the middle of his 23 years in office as Archbishop of Westminster a Gallup poll revealed that the demographic profile of Catholics, who make up 11 per cent of the population, was almost identical with that of the rest of the population. By contrast, polls from the 1950s had shown Catholics to be predominantly poor and working class.

A wide variety of social and economic factors were involved in the transition, not least the Education Acts of 1944 and 1959 by which the state funded Catholic schools, and a new generation of university-educated, confident, middle-class Catholics began to emerge. Yet even if this new generation did not feel estranged from the mainstream of national life, there were those outside the Church, not least in the British upper classes, who continued to regard it as slightly alien. Basil Hume, it is agreed both by those from such a social background and by his Catholic peers, did much by his presence to dissolve that hostility over the past few decades.

It was partly his family and school background which reassured. But there was also something about him that made the old theological arguments of the Reformation seem redundant. Like Cardinal Newman before him, he showed that it was possible to be English and a Catholic, and unlike Newman he did not have to convert to prove it. "He had an air which was somehow pre-Reformation," one Anglican peer said. "You sensed that when he went into one of the medieval cathedrals he belonged there, and yet in a thoroughly modern way."

It was a synthesis of which Hume was conscious, and of which he was never more proud than when, just weeks before his death, he went to Buckingham Palace to receive the most prestigious award in the monarch's personal gift, the Order of Merit which she bestows on individuals she regards as being of "exceptional distinction". After the private ceremony the Queen talked at length with the dying priest she had referred to as "my cardinal" ever since she made a historic visit to Westminster Cathedral for Latin vespers in 1995. After he left Hume made a point of saying: "I would like to think this is a recognition of the part played by Her Majesty's loyal Catholic subjects - laity, clergy and bishops - in the life of the nation."

But Hume's impact was much wider than on how his Church related to wider society. For Catholics his key role was as a mediator between Rome and his flock. In a period in which Pope John Paul II became more reactionary in his attempts to shut down debate within the Church, Basil Hume strove to preserve the improvements that the Second Vatican Council had brought when it discarded the model of a Church turned in on its own sacramental life and instead looked to embrace what was good in the secular world and to change what was not.

There were those who felt Hume did not do enough. Pope Paul VI had hinted before his death that more change was needed - with the Church reforming its hierarchical structure, practising poverty, enabling greater participation by the poor and behaving more justly towards its members. Some Catholic "progressives" were disappointed that Hume did not press for movement here. Advocates of women's ordination, peace campaigners and members of the support groups for priests who had left the ministry were all cold-shouldered.

But pressing for radical change did not suit Hume's cautious temperament. Nor did it seem prudent to allow others their head at a time when Paul VI's more authoritarian successor was suppressing "dissent" across the world by appointing conservative bishops and silencing theologians who did not share his revisionist views. Equally Hume was keen to rein in the small disgruntled lobby of English conservatives who tried to foment the kind of polarisation which has dogged the Church in Holland, Austria and the United States. When they brought the right-wing American television-evangelist nun Mother Angelica over for a rally Hume shrewdly attended, and chastised them for their attempt to drive a wedge between Rome and the English bishops. "It is not possible to express loyalty to the Church without including loyalty to one's own bishop," he told them.

Basil Hume's death thus leaves English Catholicism delicately poised. Its new leader - to be appointed by Rome after it receives a terna, a list of three recommendations from the Wimbledon-based papal nuncio - might be someone with the skills to consolidate its position in British national life. It might be someone chosen to transmit more directly the policies and prejudices of the centralised Vatican bureaucracy. It might be someone whose skills would be thought primarily to fulfil the central episcopal task of being a pastor to the priests of Westminster.

Balancing such competing priorities will be the task of the nuncio Archbishop Pablo Puente, one of the Vatican's career diplomats. For many weeks now he has been taking soundings from prominent English Catholics, including the 23 diocesan bishops. On the basis of that he will, in the coming weeks, submit to Rome three names, in order of preference. It will then be up to the Congregation for Bishops whose prefect is a centre-right Brazilian Dominican, Cardinal Lucas Moreira Neves.

In Rome the two tipped candidates at present are Bishop Vincent Nichols, who for the past seven years has been Hume's auxiliary bishop in north London, and Fr Timothy Radcliffe, the Rome-based Master of the Dominican order. The pair offer an interesting contrast. They are both aged 54, both warm and outgoing, both good with the media, and both have an engaging humility and a well-honed skill at diplomacy. But Nichols is a Liverpudlian grammar school boy where Radcliffe, who is from one of England's oldest Catholic aristocrat families, went to Downside. Yet both fulfil Vatican officials' wishes for the job to go to someone with experience of Rome.

Nichols is a diocesan priest who is every inch the church diplomat - a former general-secretary to the bishops' conference in England and Wales, an adviser to Cardinal Hume and the late Archbishop Worlock of Liverpool at synods in Rome for 20 years, and a delegate in his own right to the last Bishops Synod in 1994. Hume himself is said to have named Nichols as his preferred successor, but then the cardinal is said also to have pushed, without success, for Nichols to be made Archbishop of Liverpool in 1996. Since then, however, Nichols was appointed as a papal representative when the bishops of the island Churches of the Pacific gathered in Rome last year. Even more significantly, Pope John Paul nominated Nichols as one of the 15 members of a council to prepare for a special assembly on Europe to be held in Rome in October; among the other members was the Vatican's guardian of doctrinal orthodoxy, Cardinal Joseph Ratzinger. His peers regard him as "ambitious, but for God rather than for himself".

Radcliffe is an altogether more flamboyant character. In his early years he was seen as a bit of a maverick but since taking over as top Dominican in Rome he has won great respect in all quarters. He is a man of evident spirituality. He is a good communicator. His fellow Dominicans say he is efficient, diligent and manages to combine humility with being inspirational. He is well liked by the Pope. He has recently done battle, and won, over who should succeed as head of the Institut Biblique in Jerusalem after Vatican officials tried to veto the order's choice. His chief disadvantage is that he comes, like Basil Hume, from a religious order; parish priests in Westminster would like to see someone with parish experience, such as Nichols.

The same reservation would apply to another candidate mentioned in Rome: Fr Michael Fitzgerald, the secretary of the Pontifical Council for Inter-religious Dialogue. Indeed, Fitzgerald has ruled himself out on the grounds that, though he was born in Manchester, as a White Father he has spent most of his time abroad as a missionary and then in Rome as a Curia official.

Several of the names often mentioned in the English press are not seen as strong candidates in Rome. Patrick Kelly, 60, the Archbishop of Liverpool since 1997, is a prayerful man of sound common sense and the pre-eminent theologian among the English bishops. But it is felt too soon to move him from Liverpool where he is becoming well liked by the diocesan priests who were left without a bishop for over a year before his appointment. Timothy Wright, the Abbot of Ampleforth, is deemed to be insufficiently experienced, as is Peter Smith, Bishop of East Anglia.

There is one other serious option. If Nichols or Radcliffe were to get the job, they would be in post for more than 20 years, since Catholic bishops retire at 75. If it is deemed that they would be better, more experienced candidates next time round, then there are two older candidates being mentioned in Rome. One is Cormac Murphy-O'Connor, Bishop of Arundel and Brighton, 66, a former rector of the English College in Rome who has astutely handled the Church's discussions with Anglicans for the past 16 years. The other is David Konstant, Bishop of Leeds, 69 this month, who impressed the Vatican during the long process of preparing the Church's updated 1991 catechism.

Where Rome strikes the balance on all this will depend on what it sees as the key issues facing the English Church in the millennium. It will not be Basil Hume's agenda. The three things he proposed for discussion for the October synod in Rome were the issue of communion being denied to divorced and remarried Catholics, the reintegration of priests who left to get married, and how the Church can do more for women - "unless we do more, we'll lose our best women," the late cardinal told his advisers. All three issues find no place in the synodical debates.

So what are the Vatican's priorities for Hume's successor? He should, apparently, be adroit on ecumenical relations with other Christians. He should be able to take a strong stance on social and ethical issues - and, apparently, be more aggressive on war than Hume was seen to be. He should realise that the nation needs to be reconverted to Christianity. And he should be able to dialogue with secularism.

Finding someone who could fulfil the brief on issues that pull in such different directions will be a tall order. The choice that is eventually made will give some indications as to where Rome's priorities lie.