As the hopes of a majority died, the feelers went out

David Cameron sat down in the Thatcher Room on the third floor of the Millbank Tower at 3.45pm yesterday and made the most important telephone call of his political life. It was to Nick Clegg, the Liberal Democrat leader, and it was to offer him a coalition that Mr Cameron hoped could put both men in power for the next five years.

Half an hour earlier, Mr Cameron, wearing a dark blue suit and a light blue tie, strode into the St Stephen's Constitutional Club in Queen Anne's Gate, Westminster, and announced his plan to offer an alliance to Mr Clegg's party to try to create stable government.

"Nick Clegg has said that because the Conservative Party won the most votes and the most seats in this election we should have the chance to form a government, and I thank him for that," he said. "So we will now begin talks with other parties to see how that can be done."

He knew that the groundwork for the talks had already been laid by Ed Llewellyn, the Tory leader's chief of staff, and Oliver Letwin, the head of policy. They had acted as the conduits in telephone calls to the Clegg camp over the previous 24 hours as the prospect of a hung parliament began to materialise to tease out a possible deal.

Mr Llewellyn is an old friend of Mr Clegg and his wife, Miriam Gonzalez Durantez, who used to work with Mr Llewellyn in the former EU Commissioner Lord Patten's office in Brussels. Conveniently, they also shared an office with Lord Mandelson's press secretary, Peter Power, in Brussels. Steve Hilton, the master strategist in the Cameron camp, and Andy Coulson were also heavily involved in thrashing out the offer to the Clegg camp.

Mr Cameron shares the square office with his friend, George Osborne, the shadow Chancellor. Their desks overlook the atrium in the modern tower block by the river Thames where the Tories have their headquarters. Also in on the contents of the call were Mr Osborne, Mr Llewellyn, who has his office across the corridor from the leader's suite, Mr Coulson and Mr Hilton.

Mr Cameron described his offer to the Liberal Democrats as "big, open and comprehensive". It dealt with the four key issues on which Mr Clegg fought the election – a cross-party committee to come up with proposals for electoral reform, reform of the tax system, a pupil premium in schools, and a low carbon economy.

How far Mr Clegg is prepared to accept Mr Cameron's offer of a review of electoral reform – which senior Liberal Democrats regard as nothing more than kicking it into the long grass – is likely to determine whether their talks stand or fall. But in the careful choreography by the two leaders, both Mr Clegg and Mr Cameron spoke in similar terms yesterday, emphasising that politics had "broken" and there was a need for them to rise above party interest to work together.

Mr Cameron also set out the Tory sticking points: strong defence, by which he meant he would not accept Mr Clegg's plan to scrap the Trident nuclear system; and not being "weak" on immigration, such as the Liberal Democrat commitment to offer an amnesty to 600,000 illegal immigrants in Britain.

"So I think we have a strong basis for a strong government. Inevitably the negotiations we are about to start will involve compromise – that is what working together in the national interest means," said Mr Cameron.

A senior Conservative figure involved in the negotiations confirmed Mr Cameron was prepared to offer a coalition, with seats in the Cabinet, to secure a deal with Mr Clegg. "We are prepared to discuss it. We not excluding anything," he said. "If all this falls through, we might form a minority government. But we want something stable that lasts."

Both Mr Clegg and Mr Cameron know that the hard part will be persuading their parties to accept any deal. And that will not be easy. The Thatcher Room, in which the call took place, is named after the Iron Lady, who would never have countenanced any pact with the Liberals in her day.

Tim Montgomerie, the leader of the grass roots activist website, ConservativeHome, joined the media circus on the green at Westminster to denounce a deal with Mr Clegg. He said the existing first-past-the-post voting system was "non-negotiable" for most Tory supporters. A survey carried out on his website showed 92 per cent of Tory supporters were in favour of "going it alone" as a minority Government.

Grassroots Tory supporters are also angry with Mr Cameron for the modernising style of his campaign. Many wanted him to be more aggressive in attacking Gordon Brown's record in office and Mr Clegg. "Agreeing to the TV debates was a big mistake," said Mr Montgomerie. "The 'Big Society' wasn't understood by anybody. And not discussing immigration was like Manchester United leaving Wayne Rooney on the substitutes bench."

The controversial non-dom Tory peer Lord Ashcroft, who spent millions of his own money in attempting to win Labour marginals, also blamed the televised debates for denying the Tories an outright victory. "I think from the time the Conservatives were ahead we then had the debates, which has quite obviously turned everything topsy-turvy, and what were natural assumptions before those debates changed the whole of the playing field," he said.

Shadow Cabinet ministers also made hostile private telephone calls about the Cameron plan to seek a deal with the Liberal Democrats. Discreet calls were also made to Tory grandees who had won their seats by fighting the Liberal Democrats to see whether they would stomach a deal with Mr Clegg. "I told them to do nothing," said one Tory MP. "I would like nothing more than Labour and the Liberals to try and stay in office for a year. I think in 12 months we would come back with a landslide."

The old warhorse, Lord Tebbit also urged Mr Cameron in a blog to "sit tight. Try to form a minority government, but not a coalition. Above all, no coalition with the Liberal Democrats, who have been far from endorsed by the British electorate."

Lady Thatcher's party chairman added: "So, David, if Mr Clegg calls on you, tell him that you are ready to form a minority government – and that you hope you can count on Mr Clegg's support, since he has previously said that the party with the most seats and highest proportion of the popular vote should form the new government. That party is the Conservative Party. As I said, sit tight."

Ed Vaizey, the Tory MP who retained his Wantage and Didcot seat, said he expected "informal and flexible" understanding with the Liberal Democrats, rather than a coalition.

Even Mr Cameron's bicycling friend, the Mayor of London, Boris Johnson warned against giving away too much to the Liberal Democrats in his own colourful terms. "Whatever type of Wall's sausage comes out from this, the dominant meat has got to be Conservative," he said.