Racing around the flooded North of England after David Cameron, you get just a glimpse of what it might be like to live the strange life of a Prime Minister. His schedule changes by the hour, with snatched meetings in cars, hotel rooms, even a couple on a footbridge over a bulging canal. The leap from senior frontbencher to leader (let alone Prime Minister) is a massive one in terms of pressure, prestige, profile. So, David Cameron, we wondered, do you have any tips for Gordon Brown?

Mr Cameron laughed. “Unbelievably tough diary control,” he said. “You are juggling an awful lot.” And enough sleep, he added, looking slightly tired.

Both men have young families. “Lots of people say you can’t combine leader of the Opposition with being a good father,” Mr Cameron said. “You can. You lay down strict rules and stick to them. Last night I got home and bathed the kids. Once a week I try to get home and bath and put the kids to bed. People say, you will not be able to do that as Prime Minister. I don’t think that’s right.”

It’s an odd situation, advice from the young pretender to the new Prime Minister, but as Mr Cameron pointed out: “I am now the longest-standing leader of a major British political party.”

Gordon Brown's Black Wednesday

The Northern Rock disaster has torn away any remaining credibility the Prime Minister had

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We met yesterday afternoon for Mr Cameron’s first interview since Mr Brown’s elevation to the premiership. As the flood waters slowly ebbed away in the Leeds canals, he was greeted with a mixture of nervous adulation from party members and rude disinterest from people recognising him as they walked by. He appeared confident, unfazed by the succession two days earlier of a new Labour Prime Minister against a backdrop of falling polls for the Conservatives.

The Tory leader is rumoured personally to dislike Mr Brown, unlike Tony Blair, whom he has made no secret of admiring. No longer is British politics going to be a contest between Blair and someone once dubbed “heir to Blair”, but between men of different generations, class, schooling and approaches.

“We both have a sense of humour,” he said of Mr Blair, recalling their fierce bouts at Question Time. “There’s a slight rapport, I suppose. We kicked nine bells out of each other, but it had touches of light and shade.”

On Monday they were both in the Commons for a statement on Europe and bumped into each other on their way out of the Chamber. “When I walked out after the statement I said, ‘What on earth am I going to ask you on Wednesday?’ He said, ‘What on earth am I going to say?’ ” It was partly Mr Blair’s “incredible mastery of the Commons” that prompted Mr Cameron to leap to his feet at Question Time on Wednesday, urging his backbenchers to join in the standing ovation for the Prime Minister.

For a moment, as he stood urging them up with his arm, it provided a stark visual reminder of the man on his own in front: leading, with some in his party following reluctantly.

He hadn’t planned to do that.

“When I saw this was a send-off I just stood up. I thought it was an appropriate send-off in a way. And I thought he was very good. His performance that Wednesday was extraordinary.”

Now Mr Cameron must deal Mr Brown, a very different prospect. Was he nervous of the big clunking fist? It would be “really interesting” to face a new opponent across the Dispatch Box. Daunting? “Of course.” Did he reckon that Mr Brown had the wit of Mr Blair? “I just don’t know the guy well enough. I always find his style at Treasury Questions rather depressing. You ask a question about how you can work together to solve the debt in the developing world, and ten minutes later he’s still stamping on your head.”

He doesn’t underestimate his opponent for a moment, he said. “I never have. I think it’s going to be a very tough battle for the future of Britain. I look forward to it.”

That battle has begun: on Tuesday one of his own MPs, Quentin Davies, jumped ship and joined the Labour Party the day before Mr Brown became leader. He issued a stinging rebuke to Mr Cameron on parting, accusing him of “superficiality, unreliability and an apparent lack of any clear convictions”.

“I wasn’t surprised,” Mr Cameron said, after a long sigh. “I knew he was unhappy.” He threw the letter into the bin after reading it. “It was the same when Shaun Woodward [crossed the floor] – as a member of the public, my reaction is, God, aren’t politicians dreadful. How can you do that to all those people who have worked so hard?”

Mr Woodward joined the Cabinet this week, being handed the Northern Ireland portfolio in a move many regarded as blatant tokenism by Mr Brown. Would Mr Cameron join the “Cabinet of all the talents” if asked; advise it, perhaps? He looked astonished and laughed. “No!”

But surely the swipe about lack of substance must have hurt? It enunciated what those in Labour hope is the biggest divide in the public image of him and Brown, between the conviction of the dour Scotsman and the slick Etonian.

He is caustic about the new Prime Minister’s style. “There’s nothing so far that Gordon Brown has said or done that has made the heart skip a beat. Most people will look at the Government and think, it’s the same old faces in different places. I don’t think there’s going to be a sense of change,” he said. “He’s always producing initiatives, quite gimmicky initiatives that die before they get anywhere. I think people are quite sick of this, the kind of McPolitics.”

Instead Mr Cameron has promised an “unremittingly positive agenda”: in weeks to come, as his policy commissions report, “the whole contention that there’s not enough substance in the Conservative Party will be knocked away.”

Mr Davies’s accusations about a lack of substance were “ridiculous” and “completely wrong”, he said.

“You have to prove to people over time what your vision is and how serious you are.”

It turns out that Mr Cameron had more reason than usual to ignore Mr Davies’s letter: he was – and he was extremely reluctant to talk about this, but we kept prompting him – at the bedside of his five-year-old son, Ivan, who is profoundly disabled and currently in hospital for two weeks having his drug regime adjusted.

Mr Cameron spent most of Tuesday at his bedside, apart from a brief lunch with Arnold Schwarzenegger (see what we mean about the strange life?). Doctors are trying to reduce Ivan’s medication, to balance treatment with “making sure he has a good quality of life and development”. “It's difficult," said the leader of the Opposition, right now just Ivan's father, “because withdrawing from any drug isn't nice . . .” His voice trailed off.

“It was really good to spend time with him,” he said. And then the Quentin Davies letter arrived in the middle of the afternoon. “It went in the bin slightly faster than it might otherwise have done.”

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