The explanation was simple, Richard Holloway, the former Bishop of Edinburgh, said in his introduction to the service. Mr Cook was indeed “a devout atheist” but he was also “a Presbyterian atheist”. That is, the Church of Scotland, which has been the backcloth to so many Scottish lives, had helped to mould him; it had given him his “moral seriousness and his flinty integrity”; and, since his father had been an elder of the kirk, “the DNA is there ”. He would, thought Bishop Holloway, have regarded the ceremony with the same kind of “affectionate irony” as he would the singing of the Red Flag at a Labour Party conference.

This was a highly political funeral as well as a Church of Scotland affair. Outside a crowd of remarkable size had gathered behind the barricades along the Royal Mile, to bid farewell to a politician of high principle. Inside, row upon row of this ancient church were filled with ministers, MPs, Members of the Scottish Parliament, trade unionists and party stalwarts.

Mr Cook’s widow, Gaynor, was flanked by Gordon Brown, the Chancellor of the Exchequer, and Jack Straw, the Foreign Secretary. John Prescott and his wife completed the row. Behind them sat John Reid, Neil Kinnock and David Blunkett. Opposite, across the well of the church, were Patricia Hewitt and Tessa Jowell. Clare Short and Stephen Byers were there. It was, suggested one onlooker with some justification, “the Labour Party at prayer”.

Thus, when Mr Brown, himself a son of the manse, climbed into the pulpit to deliver his address, politics and religion seemed momentarily indivisible. The Chancellor’s tribute was part sermon, part political oratory, made more powerful by the fact that for 20 years or so his relationship with his colleague had been, at best, fraught.

Few people can remember the origins of the Cook-Brown split, but it went deep. Latterly, however, they had come together again, and no one, listening to Mr Brown’s stirring words, can have doubted that he would have welcomed Mr Cook into a future Cabinet.

I lost count of the number of times Mr Brown referred to “social justice”, to the principles of the Labour Party and to Mr Cook’s inflexible commitment to democracy. He reminded us that this was the church where one Jenny Geddes, a furious member of the congregation, had, in 1637, hurled her chair at the pulpit in protest against the new Prayer Book introduced by Archbishop Laud. “No one in this congregation will have any doubt on whose side Robin would have been, ” he said.

Perhaps the most eloquent passage came when he quoted Sophocles: “One must wait until the evening, to see how splendid the day has been.” Then he added: “Perhaps sadly it is only over the last week since Robin’s time has ended that we have come to recognise the breadth and depth of an astonishing life of service . . . . I believe it could be said of all of us that we did not value Robin enough in life.”

Both Mr Cook’s sons, by his first wife, Margaret, took part. One of them, Chris, read from his father’s recently published diaries, The Point of Departure, and the other, Peter, gave a reading from Émile Zola that recalled Mr Cook’s hopeless culinary skills, and remembered him once setting fire to a wastepaper basket as he attempted to burn some leaked documents.

But perhaps the most moving moment of the whole service came when the Scottish fiddler Aly Bain and accordionist Phil Cunningham electrified listeners by playing the Internationale. It is not every day that you hear the Communist anthem played in a cathedral, but by the end of it most of the congregation was humming the tune in the background — an extraordinary sound.

There was, of course, one noted absentee. In the normal course of events, no one would have dreamt of drawing attention to Tony Blair’s decision not to attend. But in the normal course of events, no one would have dreamt of asking John McCririck, the Channel 4 racing commentator, to deliver an address. The idea had been for him to speak about Mr Cook’s love of racing. Instead he launched an attack on the Prime Minister, accusing him, from the pulpit of the cathedral, of “ petty vindictiveness” for staying away, and contrasting his absence with Baroness Thatcher’s appearance at Sir Edward Heath’s funeral. There was an almost audible groan from the congregation as he spoke. “There is a time and a place for that kind of thing,” one MP said. “And this is not it.” “What a bampot,” muttered another (bampot being a peculiarly Scottish word for idiot.)

Afterwards, as the mourners streamed across the High Street to the City Chambers, there was almost universal agreement that McCririck’s outburst had been, at best, “inappropriate”. Clare Short, Chris Smith and Margaret Cook, all concurred in saying it had been out of place, and detracted from the dignity of the occasion. Charles Kennedy, the Liberal Democrat leader, agreed, adding, however: “I think what people up here will have resented most was bringing Lady Thatcher’s name into Robin Cook’s funeral service.”

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