Mr Cameron was speaking at the annual Westminster Correspondents dinner before an audience of journalists.
The event - revived for the first time since 1974 - was an opportunity for Mr Cameron to show off his sense of humour and poke some gentle fun at his tormentors in the press.
Looking out at the crowd of reporters dressed up in black tie in the grand surroundings of the House of Commons Members' dining room, the PM quipped: "The last time I was at a dinner this posh, Boris (Johnson) spent the rest of the night in prison."
Tongue firmly in cheek, the PM recounted a day spent canvassing with the London mayor, when a woman answered their knock on the door with the words: "Boris, you're the father of one of my children."
A moment's horrified flustering by Johnson was ended as she added: "It's your daughter, I'm her maths teacher."
The assembled press, eager to hear Mr Cameron's plans for 2014, pricked up their ears and licked their pencils as he said he was ready to announce "my priorities for the year ahead".
"Number one," he said. "Keeping the bald spot under control."
He insisted he had not known in advance that his hairdresser was getting an MBE in the New Year's Honours but he added: "If you can make cuts and stop recession at the same time, you deserve an honour."
His other two priorities, he said, were keeping the coalition on the road while Nick Clegg "the product of the mean streets of Westminster and Cambridge", tried to differentiate himself from the public-school Tories, and keeping Lib Dem Home Office minister Norman Baker off the television.
He had some acerbic words for his own party, noting that after press reports of a letter from 95 Eurosceptic backbenchers, "the only problem was that there was no letter, they didn't send it and it didn't have 95 signatures".
He praised backbencher Penny Mordaunt for her decision to appear on ITV's Splash to raise money for charity, adding: "If every Tory MP who's taken their clothes off in recent years had had such noble intentions, we would be in a much better position."
He even had kind words for his greatest adversary in the House of Commons - shadow chancellor Ed Balls - with whom he claimed to have a lot in common.
"We both love The Sound of Music, we both love Delia Smith - for different reasons - and we both like the Antiques Roadshow," he said. "I like it for the heartwarming stories, Ed likes it when they sell the family silver."
Mr Cameron ended with praise for Britain's tradition of a free and fearless press, paying tribute to The Guardian's parliamentary sketchwriter Simon Hoggart, who died earlier this month.
"At its best, the British press and the political press has a vital role to play in our country," said the Prime Minister.
"Tenacious, uncontrollable, sceptical, often uncomfortable for us politicians, British political reporting is deservedly respected around the world for the way it probes, inquires and scrutinises. These things are lynchpins of our democracy."