Standing in his kitchen in North Kensington – not Notting Hill, says his press officer wearily – the man who hopes to be our next prime minister is dying to tell me something. “Can we tell her yet? Can we tell her?” he keeps asking his spokesperson, Gabrielle Bertin – or Gabs, as he calls her. A group of sullen Poles traipse in and out, dismantling a marquee from a champagne party for Tory donors the night before. I wonder what has happened. The Conservative leader is clearly agitated, but is he excited or cross? Ready for the day in a dark-blue Paul Smith suit, he grabs his overnight holdall, handful of ties and gaping black briefcase of papers, and we just about get in the car before he can keep quiet no longer. “Remember we were worried it would be boring for you following us around?” he says, referring to my usual beat as a foreign correspondent – the last opposition leaders I travelled with were Benazir Bhutto in Pakistan on the day she was bombed, and Zimbabwe’s Morgan Tsvangirai, who has narrowly survived three assassination attempts. “Well, now we’ve got our own bombshell!”

It turns out that David Davis, his shadow home secretary, confided in him the previous night that he would be resigning his seat in the Commons after the opposition narrowly lost to the government on legislation to detain terror suspects for 42 days. That afternoon Davis would publicly announce his decision and his plan to fight a by-election on the issue. “But that doesn’t make sense,” I say.

“Yes, it’s odd; that’s what I thought,” Cameron nods. “Brave but odd. Now I have to decide what to do about it.” At Northolt air base, a six-seater plane is waiting, lent by a wealthy donor. Cameron disappears with his phone to sound out his closest advisers. When he reappears, he is flanked by three other women: Kate, Liz and Rachel. Like Gabs, they are all glamorous, well spoken, clutching beeping BlackBerrys and clad in short skirts showing bare legs and high heels.

As Cameron strides across the tarmac, assistants tripping alongside, for a bizarre moment I think of a Bond movie. But DD, as he refers to Davis, is not Le Chiffre, and Cameron and his posse of girls are not off to save the world, at least not yet. Instead we are going to Cornwall to take on “the yellow peril”, as he calls the Liberal Democrats.

Travel with “Dave” is a jolly jape: he snacks on egg-mayo sandwiches, crisps and KitKats in the back of the car, keeps us entertained with funny voices, stops at petrol stations for “comfort breaks”, and uses expressions like “buggeration” when he loses his phone or keys. He is so determinedly upbeat that I’m astonished to learn that his iPod is filled with the Killers, Radiohead and the Smiths (though there is a bit of Lily Allen for light relief).

But it’s deadly serious. At 41, Cameron is riding higher in the polls than any Tory leader since Mrs Thatcher, with one in three voters finding him charismatic, compared with one in 100 for Gordon Brown; he has set his cap at No 10 and has no intention of being thrown off course. After all, he knows only too well what it’s like to be down. Last summer it was snooty Dave Cameron traipsing round Rwanda do-gooding while parts of his own West Oxfordshire constituency were many feet under water. Meanwhile, brave, honest Gordon was back home pushing back the floods, foiling terrorist attacks and fighting off a new outbreak of mad-cow disease. Then it was Labour seven points ahead in the polls and talk of Tories plotting a no-confidence vote to oust Cameron.

The Conservative leader claims that as a boy he yearned to be a train driver, a lorry driver or a soldier. “I certainly can’t claim I wanted to be PM from the age of six, and I think those who do should be automatically disqualified. It was that the more I worked in research in the back room, the more I thought it was something I’d like to do in the front room, rather than some Heseltinian plan on the back of an envelope.”

But he says his early school years, pre-Eton, were ideal grounding. “I went to a small junior school where we lost every game. It was good preparation for being in the Tory party.” (That “small junior school” was Heatherdown preparatory school in Berkshire, attended by Princes Andrew and Edward.)

The Conservatives may be a whopping 20% ahead in opinion polls, which would give them a crushing election victory, just as they enjoyed in the June by-election in the former Labour stronghold of Crewe and Nantwich. But Cameron tells his troops almost daily: “There is no place for complacency.” He has targeted 100 marginal constituencies that they must secure to win the next election. Hence our two-day visit to Cornwall, where the Conservatives currently don’t have a single seat.

Because of the Davis issue, we are running late. Not that he would know, as he doesn’t wear a watch. The Cameron girls start to fidget as we sit on the runway, precious minutes ticking by. The pilot explains that we must wait for the landing of a big grey C-17 transport plane – the advance party bringing limos for President Bush, who is arriving a couple of days later.

“The day is turning into a vale of tears,” jests Cameron as he opens the yellow file his research department has prepared for his trip. It is divided into sections such as Deep Sea Fishermen and lists key local issues such as killing badgers to prevent the spread of bovine TB to cows, Cornish identity, and racism (a pig’s head had been recently nailed to a chapel near Truro that was set to become an Islamic community centre). Cornwall is one of the poorest parts of the country: his research says a third of households have nobody in full-time employment. This is the perfect target for Cameron’s new caring Conservatism, and he points out to me that five of the party’s six candidates in the area are female (the other is a man with a ponytail).

As the plane finally heads up into the clouds, he is finding it hard to concentrate on the plight of fishermen while he must decide how to respond to Davis’s resignation before the news is announced. In the three years since he became party leader he has worked hard to re-establish unity in the party, and the last thing he wants is this to be seen as evidence of old divisions resurfacing. That day’s papers are full of 26 dolphins dying in a Cornish river where they were stranded, and he wonders about distracting people from the Davis issue by wading in and helping to save the others. “Muscular Conservatism, that’s what we need,” he jokes.

Times Recommends

• 6 reasons not to give gifts this Christmas
• Remembrance Day: All the lonely heroes