David Cameron has for the first time publicly denied allegations made in a biography written by the former Tory donor Lord Ashcroft that he was involved in a bizarre university club ritual with a dead pig’s head.

The prime minister said everybody could see straight through the book published by Ashcroft, and confirmed he was disputing the specific allegation that he put a private part of his anatomy in a dead pig’s mouth at an event of the Piers Gaveston Society when he was a student.

The book, co-written with the journalist Isabel Oakeshott and serialised in the Daily Mail, has made international headlines with its allegations about Cameron’s lifestyle, including stories about him smoking cannabis with friends at Oxford University and cocaine allegedly being in circulation at a party hosted by the Camerons.

The book alleges Cameron knew about Ashcroft’s tax status as a non-dom in 2009, despite the prime minister having previously said he only knew about it for a month before it was made public in March 2010.

Ashcroft, who donated millions of pounds to the Tories before 2010, admits having a “personal beef” with Cameron for not giving him a ministerial job when the coalition was formed but he insists the biography is not about settling scores.

Asked about his feelings towards Ashcroft and the pig allegation, Cameron said: “Everyone can see why the book was written and everyone can see straight through it. As for the specific issue raised, a very specific denial was made a week ago and I’ve nothing to add to that.”

In fact, Downing Street has said nothing about the anecdote on the record, although Conservative sources have described the book’s claims as “utter nonsense” and “untrue”.

In the days after the Mail began serialising the book, Cameron joked about the biography at a dinner, saying he had been for a minor surgical procedure that involved “just a little prick, just a stab in the back”, which he said rather summed up his day.

The hunt is now on for the Tory MP – an Oxford University contemporary of Cameron – who claimed to the authors of the biography that he had seen photographic evidence of the pig incident.

Mark Field, one of the handful of possible MPs, issued a furious denial that he was the source. “I regard any insinuation that I have done this as defamatory,” he told the Sunday Times. “I categorically deny it. I didn’t even know Cameron at university. I was never in the Piers Gaveston club.

“The first I ever heard of this fantastical story was when I read it in the papers. I never even heard the rumour. The whole thing is nonsense start to finish.”