What happened next highlighted the styles of the two finalists. At 9.30pm Mr Hague and close allies left for the Palace of Westminster and the suite of offices reserved for the Leader of the Opposition. The idea was to waste no one's time, "to start work straight away" as one had it. The message was deliberately Blairite - here was a young man anxious to get on with the job, to reform his party and get it back into power.
Mr Clarke, the Conservative politician with whom voters most easily identify, went off with some pals to Kennington in south London to eat at an Indian restaurant called Gandhi's.
The melodramatic leadership contest had had something for everybody: cabals, back-stabbing, deals and treachery. But the most influential happening in the triumph of William Hague was the collapse of the most surprising element of all: the so-called "Molotov-Ribbentrop pact" (named after the alliance between Germany and the Soviet Union in 1939) between Mr Clarke and John Redwood, who had nothing in common except a desire to run the Conservative Party.
The Hague camp's suspicions were aroused on Tuesday evening when Mr Redwood arrived late for a meeting with Mr Hague at the home of a former MP, Barry Legg, in Chapel Street, Belgravia. Mr Redwood admitted he had already spoken to Mr Clarke and showed only limited interest in discussing details of a possible alliance with Mr Hague. "He didn't ask for a job, he didn't seem interested. We knew then there must be a deal with the Clarke camp," an aide said.
On Wednesday press sources tipped off the Hague camp about a Clarke/Redwood press conference scheduled for Church House, round the corner from the Commons. At first glance, the deal looked like a master-stroke. Mr Clarke and Mr Redwood represent each end of the left-right spectrum in the Conservative Party on the crucial issue of Europe. If they could work together, peace would reign. By contrast, Mr Hague would insist on collective responsibility, meaning that shadow ministers would have to stick to his decision to rule out membership of EMU for 10 years. Mr Hague had begun as the compromise candidate and the two had neatly turned the tables on him.
But the Church House conference was an augury. In the hall the Redwood backers were greatly outnumbered by Clarke-ites. Neither Mr Clarke nor Mr Redwood fluffed their lines, but their body language did not speak of a warm relationship. Mr Redwood gave a taste of what the strange new order might look like: "When we disagree we will have a jolly good argument before we decide what the line will be. He is the leader, but I am not bad at arguing." More revealing still was the news that he would be Mr Clarke's shadow Chancellor.
The Hague team sprang into action determined, as one source put it, "to beat news with news". They seized on the Redwood job appointment as evidence of an underhand deal, and immediately contacted their stage-builders to set up a backdrop for a rebuttal that afternoon.
Their second line of attack was through Lady Thatcher. She had been alerted at 10am on Wednesday of the impending Clarke/Redwood pact and watched it being announced live on television. She went "absolutely ballistic". This was not the first contact with Lady Thatcher. Mr Hague had tried early in the campaign to enlist her support, but now the pleas came in thick and fast, from Alan Duncan, Mr Hague's close ally, and from newer supporters such as John Whittingdale, Lady Thatcher's former political secretary. Unwilling to back him before, this was an urgent matter of ABC - anyone but Clarke. In the afternoon Mr Duncan contacted Michael Portillo, the former cabinet minister, who also pledged his support.
Shortly before his 5pm press conference, Mr Hague's team got word that Lady Thatcher had agreed to pose for photographs with him, and 45 minutes later, before astonished and delighted tourists, Lady Thatcher appeared on the steps of St Stephen's Gate and endorsed Mr Hague. Then she toured the tea-room, lobbying right-wing MPs including Oliver Letwin and Sir Richard Body. Around 40 pro-Hague MPs joined the trawl. Messrs Portillo and Lamont hit the phones. Michael Howard and Michael Ancram lobbied the Daily Telegraph and the Times.
Overnight, the lobbying went on remorselessly, and by Thursday morning Mr Clarke's supporters were growing alarmed. Mr Hague sent copies of supportive leaders in the Telegraph, the Times and the Sun to every Tory MP with a hand-written appeal for their vote. "The future of the Conservative Party is at stake today," he wrote. One Clarke-voter said: "I could sense the disloyalty of people who pledged support to us. Some of those who had urged Redwood to do a deal with Clarke lost their bottle. They couldn't stand the pressure from Thatcher, Portillo and Lamont saying that the end was nigh." Worse, some who supported Mr Clarke in the first ballot were put off by the idea of a pact with Mr Redwood.
But most Tory MPs thought the election was still too close to call. One strategist said: "Throughout the day we wavered from pessimism to optimism. We thought it was on a knife-edge - plus or minus two or three." Francis Maude, a Hague-backer who was John Major's whip in the 1990
leadership election (when he predicted the outcome accurately) thought his man had lost. At 5pm the campaign team, and Mr Hague's fiancee Ffion Jenkins, assembled in his Commons room, to discover that Mr Maude's calculations had been wrong. Mr Hague won by 92 to 70, and became the youngest Tory leader for 200 years.
Mr Hague's rise has been meteoric and he is still largely an unknown quantity, but it is certain that one consequence of his victory will be a revolution in Conservative Party structures and communications.
His first act was to recall Lord Parkinson to be chairman of the Conservative Party. Lord Parkinson, who had supported Mr Hague, was approached at the Central Office party immediately after Mr Hague's victory. "If you're surprised, that makes two of us," he told party workers on Friday. To some the decision to recall such a veteran figure (he left the chairmanship in 1983) jarred with Mr Hague's stated ambition to double party membership with people younger than himself. But among Conservatives Lord Parkinson remains popular and could fulfil a role similar to that of Lord Thorneycroft, Margaret Thatcher's first party chairman.
Lord Parkinson was probably not the first choice, but Mr Portillo had made it clear that he did not want the job. Tories were divided as to his reasons: desire to re-charge his batteries away from politics, to make some money or to concentrate on the hunt for a safe seat being the three most common theories.
Never the less, the chairmanship is crucial in Mr Hague's plans. Modernisation of the party was part of his platform and several MPs voted for him simply because Mr Clarke is not an enthusiast for a Mandelson-style communications strategy; as one source put it "he thinks it is childish".
BUT Lord Parkinson has a mountain to climb. Party membership has been tumbling for decades. The party's ramshackle structure and its fund-raising machinery are in desperate need of overhaul, and Labour will legislate to end the secrecy surrounding the funding of the party by individuals, many of whom live outside Britain.
The Conservatives are expected to move to some form of one member, one vote - for electing the party leader and to participate in other decisions - to satisfy the demand for greater democracy within the party. Paul Whiteley, Professor of Politics at Sheffield University, predicts: "William Hague will submit himself to a special meeting for confirmation. That will be a coronation, but the next leader will be chosen by OMOV."
Reforms on the scale required will shake the party to its roots. At present, each of the 600-plus constituency associations jealously guards its own membership details. They will have to be cajoled if the party is to emulate Tony Blair's successful campaign to build a mass party with a computerised national database of membership details for one member, one vote elections, and for fund-raising. Mr Hague believes that Lord Parkinson will prove the man to sell such radical changes to party activists.
Another consequence of Mr Hague's election is more fraught with danger: this is the shift to the right, particularly over Europe. In many respects the choice of Mr Hague is logical because it places the party in the hands of those whose views represent the majority of Conservative MPs. As one source put it last week: "The choice was between an inclusive agreement to differ, or an exclusive clarity; the Conservatives chose the latter. The right have won."
Early evidence supports that conclusion. Mr Hague's language has been that of healing wounds, of putting the party together again, and of rebuilding. Yet all the key jobs are in the hands of the sceptics. Peter Lilley's role as shadow Chancellor and Michael Howard's job as shadow Foreign Secretary ensure that the unabashed and unqualified Eurosceptic line will endure. The Conservatives will remain committed to Europe but determined to cede no further powers to Brussels.
Demands for collective responsibility place the pro-Europeans in a difficult predicament. Some, like Stephen Dorrell (who was privately highly critical of the Hague campaign only a few days ago) have accepted straight away. But Mr Dorrell has long trimmed on Europe.
For Mr Clarke, whatever he says in public, the decision to retire to the back benches reflects a revulsion at the idea of signing away his principles. As one friend put it: "Ken sat round the cabinet table with William for two years without what he believes becoming clear. Now he's told that to sit in the Shadow Cabinet he would need to sign a piece of paper on a point of principle. It doesn't add up."
Mr Clarke's presence on the back benches may come back to haunt Mr Hague. Clear opposition to a single currency may, in the coming years, become less popular, particularly within the business community. At the next election the Conservatives could find themselves supporting a policy which contradicts that of much of British industry. And Mr Blair's highly political government will probably give few more targets on Europe - its refusal to sign away controls over borders at Amsterdam being a mark of Labour's refusal to offer hostage to fortune.
MEANWHILE, Labour spin doctors say that up to five Tory MPs have informal contacts with the government side and attempts will be made to lure them into defecting. But the Government may try to exploit the internal tension by enlisting the help of prominent Tory left-wingers, such as Michael Heseltine or even Kenneth Clarke, in government bodies and projects. Mr Blair could also encourage a left-wing element of the Tory party to split off by speeding up moves towards proportional representation, possibly in time for the 1999 European elections.
While a realignment of politics is possible, the more likely prospect is that a small group will defy the party whip on Europe and some other issues, such as the constitution (where the Tory line will almost certainly harden) just as the Eurosceptics did over Maastricht. As one pro-European put it: "If Hague does insist on shadow cabinet collective responsibility, he might have a united shadow cabinet but he won't have a united party."
That, as Labour discovered to its cost early in the 1980s, can be the greatest problem of all.