The figures comes amid the greatest challenge to Cameron's premiership during his six years as PM, with his Conservative party deeply divided over the issue of EU membership.
According to the Ipsos Mori poll, 48 percent of people think the UK should have a new prime minister in the event of a Brexit, while only 44 percent believe Cameron should stay on.
Half of public (third of Con voters) say Cameron shld resign if UK votes Brexit @IpsosMORI https://t.co/bYOaVZptXx pic.twitter.com/e7sczfcicf
— Gideon Skinner (@GideonSkinner) March 29, 2016
The figures are alarming for Cameron, who is campaigning for the UK to remain part of the EU after negotiating an agreement with other member states to alter the country's EU membership agreement.
While the prime minister has stated that he will not stand down in the event of a Brexit, many believe his position will be untenable if the public rejects his call to remain part of the union, particularly given the strong Euroskeptic presence in his own Conservative party.
It has also been suggested that Cameron's days as prime minister may be numbered even if the country narrowly votes to stay as part of the bloc, with many of his own MPs and party members deeply unhappy with the manner in which Cameron has handled the debate, and may push for a leadership challenge following the June 23 referendum.
Hope, rather than fear, is reason why most Britons will vote one way or the other https://t.co/bIGf2jKtJw #EUref pic.twitter.com/6AeJRFHIfR
— Ipsos MORI (@IpsosMORI) March 29, 2016
Many were left furious after Cameron suggested Mayor of London Boris Johnson was supporting the Brexit case in a thinly-veiled attack of his fellow Etonian.
Acknowledging the deep divides in his own party, Cameron called for MPs to conduct a passionate, but respectful debate, however the Conservatives have seemingly broken into a civil war over the issue with six cabinet ministers defying the PM and openly campaigning for a Brexit.
This was followed by the resignation of former Conservative party leader and Work and Pension Secretary Iain Duncan Smith.
33% may change mind while "Leave" voters have firmer views than "Remain" voters #EURef https://t.co/bIGf2jKtJw pic.twitter.com/HrA7ZxClVh
— Ipsos MORI (@IpsosMORI) March 29, 2016
While Duncan Smith, a noted Euroskeptic, said his decision was based on the government's "unfair" budget, many believed that it revealed the bitter tensions inside the Conservative party as a result of the Brexit debate.
With three months remaining until the referendum, many remain unsure with where public sentiment stands on the issue.
While most polls suggest the 'Remain' campaign is holding a slim lead, recent data suggests the gap is closing, with an increase in support for those campaigning for a Brexit.
