The story was recounted to the authors by a contemporary of Mr Cameron who went on to become an MP.
He reportedly said the pig’s head was resting on the lap of a member of the Piers Gaveston Society – a dining club at Oxford – while Cameron carried out the act.
He even claimed another member of the group has photographic evidence of the alleged act.
But the individual who is said to own the picture did not respond to approaches by the authors.
Mr Ashcroft said: “Perhaps it is a case of mistaken identity. Yet it is an elaborate story for an otherwise credible figure to invent.
“Furthermore, there are a number of accounts of pigs’ heads at debauched parties in Cameron’s day.”
The alleged act echoes the first episode of the drama series Black Mirror, in which the fictional Prime Minister has sex with a pig live on TV.
