The Foreign Secretary Douglas Hurd, in particular, has always expressed deep scepticism about the value of such a move. But the proposals agreed on Wednesday gained London's approval once it was clear that they had considerable momentum behind them, and once Britain had ensured that any attacks would be subject to the agreement of UN commanders on the ground, according to British sources.
In 40 years of the Cold War, Nato never fired a weapon in anger. Yet the alliance is now on the brink of launching attacks against Serbian artillery around Sarajevo. 'We got to a point where the critical mass came together,' says Robert Hunter, the US ambassador to Nato.
Boutros Boutros-Ghali, the UN Secretary-General, asked Nato to approve air strikes. Warren Christopher, US Secretary of State, said he did not rule out such a move. The idea of an ultimatum surfaced in Paris. A plan was emerging.
France, with the largest contingent of troops in Bosnia, was determined to get out of the trap in which it dared not withdraw its soldiers, for humanitarian reasons and for fear of triggering a wider war. Meanwhile, the French forces were becoming increasingly disilusioned with their role, to the extent that their commander, General Jean Cot, had to be replaced.
By the time Mr Hurd arrived in Brussels on Sunday night, it was increasingly evident that the week would end either with a commitment to air strikes or a colossal row. A Nato meeting was bound to finish with such a pledge. Nothing less would satisfy the French and the Americans; nothing less would end criticism over the West's inactivity.
That evening, Mr Hurd had dinner with officials in the residence of the British ambassador to the EU, Sir John Kerr. They were joined by Sir John Weston, ambassador to Nato, just back from a meeting of defence experts in Munich. At midnight, Mr Hurd spoke to Mr Christopher for the third time that day. His conversations that evening seem to have changed his mind. Next morning, he was more explicit. 'The case for air action is very strong, provided we can find a means of doing it which produces more good than harm,' he said.
By Monday, the British government was moving quickly to try to regain the initiative over what had been a considerable change of tack. John Major made his most aggressive comments, calling for 'immediate, effective and more muscular action' to bring the bombardment of Sarajevo to an end. In the Commons on Tuesday, he echoed this line.
On Wednesday morning, an early meeting of the British, French and American ambassadors with Manfred Woerner, Nato's Secretary-General, removed many of the last obstacles. Mr Woerner opened by displaying the front pages of a number of newspapers, all predicting air strikes. Ambassadors had to reach agreement, he stressed; it was vital for the credibility of the organisation.
Where there was doubt, the French ambassador, Raymond Blot, played the role of persuader, largely through careful legal argument, said onlookers. He 'demolished' many of the arguments against action, and when the diplomats broke for lunch at 2pm, several were already telling their foreign ministries that the deadlock was over and action would be taken.
The British government faced a conundrum. Conservative MPs are split over involvement in Bosnia, a fact demonstrated by a joint meeting of the Tory backbench foreign and defence committees in the Commons last week. On the other hand, the British position was looking increasingly isolated, and obstruction would threaten the unity of Nato.
Mr Major, his leadership under question, was sensitive to charges that longstanding British policy had buckled under pressure from the French or from Nato partners. As one senior Conservative backbencher put it yesterday: 'To many, it looked as if Mr Major had become gung-ho simply at the behest of the French. If you are going to change tack like this, it is better to lead the international debate. Instead, it looks as if Mr Major is unable to say boo to a goose.'
Downing Street reacted angrily to reports that Mr Major had acquiesced in the Nato ultimatum only after a 30-minute phone call from President Clinton on Wednesday afternoon.
Mr Clinton reportedly issued a direct warning to Mr Major that the Western alliance would be sundered if the UK did not sign on. Mr Major's office countered that there had been 'no arm-twisting' and that instructions to back a tougher line had already been issued to the British diplomats on Tuesday night.
Whatever the content of the Clinton phone call to Mr Major, senior Conservatives conceded last week that the change of policy towards Bosnia was part of a foreign policy which had several components - and that keeping Nato intact was one of them.
The Franco-American paper survived largely intact. Britain, so long opposed to air strikes, was in line with its allies. The British had a separate draft paper, but allowed elements of it to be subsumed within the Franco-American version. Mr Hurd and his officials had insisted on Monday - to cynical responses from the press - that the British conditions on air strikes were not 'wrecking conditions'. And so it proved.
Several elements important to Britain were clarified. The UN commanders in Bosnia have a de facto veto over any strikes, which was 'the key', said a Brussels source, given British worries about troops on the ground. The 10-day warning period can be extended if there is a real chance of settlement with a day or so of extra talks, diplomats indicated.
The role of the peace talks was accentuated in the communique, and the US said it would become more involved. Britain almost certainly said that it would stop aid convoys, and it may also have given warnings about troop withdrawals if things get too hot.