Former chancellor Ken Clarke said he would be "horrified" if any of David Cameron's potential successors campaigned for a British exit from the European Union.
Mr Clarke, who ran against Mr Cameron for the leadership, warned contenders for the role it would be "totally irresponsible" to campaign for a vote to leave in the EU referendum campaign to secure a tactical advantage over their rivals.
As a veteran of the deep divisions caused by Europe within the party, Mr Clarke warned that another Tory civil war on the issue would lead to the Conservatives being thrown out of office.
"If we start going back to Euro-wars again then all the work that David Cameron has done to get us back into office will be completely thwarted because we'll get thrown out again," he said.
Mr Cameron's decision not to seek a third term means the EU referendum by the end of 2017 could provide a leadership candidate with a platform to rally Eurosceptic Tories behind their bid for the top job.
London Mayor Boris Johnson has refused to rule out playing a role in the campaign for an exit, sticking to Mr Cameron's position of waiting to see the outcome of the current renegotiation before taking sides.
Another potential leadership candidate, Home Secretary Theresa May, has also been linked to a role in the campaign for Brexit after her aide Stephen Parkinson quit his Government job to work for Vote Leave.
Mr Clarke told The House magazine: "I'd be horrified if any of the people likely to be contenders started saying they were campaigning for 'No'. It would be totally irresponsible for a leadership candidate to campaign for Out, simply for tactical advantage in a leadership election.
"Anybody who showed so little regard for the national interest should not be regarded as a serious contender."
He said choosing the next leader on the basis of their views on Europe would be "continuing the same insanity that's put us out of office throughout the 2000s".
In a blow to the leading candidate to succeed Mr Cameron, Chancellor George Osborne, Mr Clarke predicted that the eventual victor could be a less-fancied figure.
In a reference to his own defeats in 1997, 2001 and 2005 the Tory grandee said: "In my experience of Conservative leadership elections they're always won by some candidate that nobody had thought of until the last three or four weeks.
"I don't remember anybody who started campaigning for the leadership a year or two before the vacancy getting anywhere near it."
Mr Clarke predicted that the row over membership of the EU would continue even if there was a decisive victory for the campaign to remain in the 28-member bloc.
"Referendums never settle anything," he said.
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