A huge sigh of relief swept the corridors of Whitehall on Saturday afternoon when the Belfast declaration confirmed that the Yes vote had crossed the 70 per cent psychological barrier. And among the Northern Ireland Office coterie, too, the relief was overwhelming. One senior British source confided that just a week earlier he would have gratefully settled for 60 per cent. Mr Tony Blair's gamble had paid off.
In the immediate aftermath of Good Friday, the Ulster Unionist Party's confidence had more or less evaporated. To his immense frustration, Mr David Trimble was consistently thrown on to the defensive, forced to defend the aspects of the agreement - prisoner releases chief among them - which the government's pollsters, and the shrewd Mr Peter Robinson, had identified as of most concern to unionists. The final British poll, reported to ministers and officials on Monday, fuelled united unionist projections that the No vote might actually come close to 40 per cent.
There is little doubt that compelling evidence of unionist resistance was a major factor in Mr Blair's decision to extend his campaign visit last week. And he and his advisers will draw encouragement from the fact that the upturn in the Yes campaign was accompanied by Mr Trimble's decision to accentuate the positive, making that joint appearance with Mr Hume, and carrying the challenge to his opponents.
But while there is cause for celebration inside Number 10, the Prime Minister will know - even if Secretary of State Dr Mo Mowlam does not - that there is no cause for complacency. Certainly there is no basis for, or obvious wisdom in, the slightly triumphalist tone she adopted on Saturday afternoon when pointing to Dr Paisley's apparent failure to repeat the success of his performances in European elections.
The psychological advantage is unquestionably again with Mr Trimble. But the unionist battle for domination in the assembly is by no means over. And the actions of the British government will have a vital role in shaping the context in which that electoral contest is fought.
Dr Mowlam must shortly present Bills to the House of Commons to give effect to the Agreement's provisions for the transfer of powers to the Northern Ireland Assembly and for the programme of prisoner releases.
The Prisoners Bill is expected shortly, with the Assembly Bill likely to take its Commons stages before the summer recess and complete its passage through the House of Lords in the autumn. That would pave the way for the transfer of power to Stormont in January or February of next year. And given Mr Blair's massive majority, the passage of the legislation is not in serious doubt.
However, problems were looming on the horizon even before the referendum campaign and Mr Blair may have added to them with the assurances he found it necessary to give unionists along the way.
Specifically the Conservative Party is seeking clear "linkage" between the proposed prisoner releases and Sinn Fein assuming seats in the executive with the issue of decommissioning IRA weapons. The party has so far declined to give the government an assurance about the speedy passage of the Prisoners Bill. And Lord Tebbit is now threatening to insert a "sunset" clause in the Assembly Bill, aimed at bringing the whole thing crashing if decommissioning is not accomplished by a designated date.
Mr Jeffrey Donaldson can be expected to ally himself with the Conservatives on these issues, and to recruit them to press Mr Blair to make explicit how - in legislative form - he proposes to make good last week's pledges, including "those who use or threaten violence excluded from the government of Northern Ireland." Mr Trimble insisted, ahead of Thursday's vote, that Mr Blair had addressed all of Mr Donaldson's concerns, and that the differences between them were actually very small. But those differences will be laid bare by the parliamentary process. And the response of Mr Blair and Mr trimble to them will have important implications for the agreement itself.
While no specific timetable has yet been defined, there is no doubt in nationalist minds that the completion of the assembly election is to be the trigger for the commencement of the implementation of the agreement in all its aspects. A very early requirement is the creation of the executive in "shadow" form. Mr Trimble last week suggested this would not be necessary until shortly before Christmas, if then - prompting a warning from Seamus Mallon that failure to effect all the transitional arrangements would be to abrogate the agreement itself. As the SDLP and Sinn Fein prepare for electoral battle, Mr Blair may expect a sharp reminder that he has a wider responsibility than the management of the unionist constituency.