The allegations are contained in a new biography from former Conservative Party treasurer Lord Ashcroft, which is being serialised in the Daily Mail.
In addition to the pig head incident, said to have taken place during a party while Cameron was at the University of Oxford, Ashcroft’s book also alleges that the Prime Minister was a member of a "dope smoking group" called the Flam Club at Oxford; that he was part of an Oxford society that specialises in "bizarre rituals and sexual excess"; and that cocaine was allowed to circulate in he and his wife’s London home.
Downing Street declined to comment on the allegations, which have received widespread publicity this morning and much discussion on social media. At the time of writing, #piggate was trending on Twitter with 183,000 mentions.
PR professionals have suggested that the allegations, despite their sordid nature, will have little lasting impact on Cameron's reputation.
Jonathan Hemus, managing director of Insignia, said: "While the alleged incident is beyond the high jinks of many university indiscretions and will lead to some embarrassment for David Cameron in the short term, it is unlikely to do any substantive damage to his long-term reputation.
"Downing Street’s policy of not commenting on the story seems like the right strategy at this stage, but if Lord Ashcroft makes more damaging allegations, this may have to change. What’s for sure is that it provides plenty of material with which new Labour leader Jeremy Corbyn can torment the Prime Minister."
Jonathan Chandler, partner at Reputation Inc, said: "There have been allegations about weed going back into the past that [Cameron] managed to ride over historically.
"If there’s a sting and someone is caught out then the consequences are fairly obvious. But things that are dragged up from the 'dark and distant', especially if there’s not strong substantiation, [politicians] do generally ride them out."
@prweekuknews It will come & go and by time of Party Con he will make a jokey reference to it. But first Twitter will go into meltdown.— alex woolfall (@woolfallalex) September 21, 2015
Many people are using the pig head story to make fun of Cameron on social media this morning. Paddy Power has already 'brandjacked' the story:
There was also this post from a spoof Twitter account of the Prime Minister:
No, I didn't call her Babe No, I didn't need oinkment No, she wouldn't leave me aloin No, I've never made a rasher decision #piggate— David Cameron (@DavidChameron) September 21, 2015