Lord Heseltine has warned of a “civil war” in the Conservative Party if cabinet ministers are given a free vote in the EU referendum.
David Cameron is facing calls to allow his top team the freedom to campaign for in or out without being sacked.
But former Deputy Prime Minister Lord Heseltine said that would make Mr Cameron a global “laughing stock”.
He told BBC Radio 4’s Today programme ministers who defied the PM on the issue should resign.
Mr Cameron has promised to hold an in-out referendum on EU membership before the end of 2017, once he has secured reforms to Britain’s relationship with the 28 member bloc.
He has not ruled out campaigning for an exit – but is likely to recommend Britain remains in the EU when he returns from Brussels with a deal on his four reform demands.
Lord Heseltine, who has long campaigned for Britain to stay in the EU and remains an influential behind-the-scenes voice in the government, said it would be “naive” to imagine ministers on different sides of the debate could sit around the cabinet table “happily smiling” at one another.
“There is a collective loyalty and the consequence of having a free vote, if you like, would be that the divisions, the divisiveness, the bitterness that would flow would actually, in my view, make the prime minister’s position very difficult.
“If they feel so strongly then they should resign, although it is quite difficult for me to understand how they’re in the cabinet in the first place.”
Conservative MP John Redwood hit back at Lord Heseltine’s comments, telling BBC News: “I don’t think he understands how well people get on with each other.”
The veteran Eurosceptic said it would be “quite easy” for the cabinet to have a free vote and be “professional and come back together again”.
About “half a dozen” cabinet members believe “pretty strongly” Mr Cameron’s EU deal “won’t be good enough” and will join the leave campaign, said Mr Redwood.
And he predicted Mr Cameron would want to resign if Britain voted for exit, making way for a Conservative leader “who believes in leave” and could negotiate a favourable trade deal for the UK outside the EU.
Eurosceptic former environment secretary Owen Paterson also called for cabinet ministers to be given a free vote.
The Conservative MP said the referendum was the biggest decision facing the British people in 500 years and said it was “wholly incredible” that ministers would want to keep the country in an EU that was already pushing it to the margins.
“Personally, I think they should keep their jobs. If they are not allowed to campaign from within the cabinet they should resign.”
The prime minister said on Friday the UK would “fundamentally change” its relationship with the EU in 2016, following talks with fellow leaders in Brussels.
He is aiming to get a deal at a meeting of EU leaders in February, with a referendum to follow – current speculation is that could be held in June or July.
Several well-known government figures are thought to be flirting with an out vote, including Iain Duncan Smith, Theresa May and Boris Johnson.
Mr Cameron has held face-to-face talks with ministers including Northern Ireland Secretary Theresa Villiers and Justice Secretary Michael Gove in an attempt to maintain unity ahead of the referendum, according to The Times.
The main sticking point in talks with other EU leaders is Mr Cameron’s demand for non-EU workers to be barred from claiming in-work benefits for four years.
Downing Street ruled out making the rules apply to UK citizens – one of the suggested compromises – after official analysis found that as many as 300,000 Britons could lose out.
“We are not considering any option that would affect this number of British citizens,” a Number 10 spokesman said.
“The proposal on the table remains the one of limiting in-work benefits to EU migrants for four years with the aim of reducing the pull factors that have attracted such vast numbers of Europeans to the UK in recent years.”
About 50,000 home-grown workers would be affected if it was based instead on a residency test – but even that is reported to be opposed by some in the Cabinet, including Mr Duncan Smith.