In a warning shot to Brussels, the Ipsos-MORI survey found 74 per cent of Conservatives on the Commons benches thought keeping free movement rules after Britain leaves the EU would be “unacceptable”.

And just under 63 per cent of Tory MPs also opposed the idea of the EU Court of Justice continuing to have jurisdiction over the UK after the official Brexit date in March next year.

The findings of the poll, commissioned by the think tank The UK In A Changing Europe, will add to the pressure on Theresa May and EU Exit Secretary David Davis to take a tough stance in the next round of talks with the Brussels negotiating team.

EU chief negotiator Michel Barnier is pressing for Britain to accept continuing free movement and EU regulation throughout an expected transition period after the country quits the bloc.

Earlier this week, a report warned that up to a million more EU citizens could get the right to settle in Britain if the Government accepts the free movement demand.

Research from the population pressure group Migration Watch estimated that the move could lead to a significant increase in the numbers allowed to come into the country before new border controls are imposed.

The Ipsos-MORI poll also laid bare a damaging rift within the Labour Party over Brexit.

It found that 90 per cent of Labour MPs disagreed with their leader Jeremy Cobyn’s claim that continuing membership of the European single market was incompatible with Brexit.

The research, based on face-to-face interviews with 105 MPs, was carried out by Ipsos MORI in November and December 2017 last year.

It showed there has been a significant shift in position among Tory MPs about single market membership.

In December 2016, 44 per cent of Tory MPs felt the EU referendum result meant Britain could not remain in the single market. 

According to the latest survey, that figure has now risen to 76 per cent.

Last year, 66 per cent of all MPs felt remaining in the single market was compatible with respecting the referendum result compared with 56 per cent in the latest poll.

Eighty-five per cent of MPs on both sides of the Commons backed the proposal for a transition period after Brexit but were divided over how long it should last. 

Only 12 per cent of Tories believed the period could be “open ended” while 45 per cent of Labour MPs backed such a flexible option.

Just under two thirds of Tory MPs (65 per cent) agreed with the statement “no deal is better than a bad deal” but 77 per cent of Labour MPs rejected it.

Tory MPs were also overwhelmingly positive about Britain’s prospects outside the EU with 89 per cent believing the economy will get better over the next decade.

More than 80 per cent of Tory MPs thought the UK will be able quickly to sign trade deals with countries such as China and the US and 54 per cent thought such deals would more than compensate for any loss of trade with the EU.

Professor Anand Menon, director of The UK in a Changing Europe, said: “Brexit presents a stark challenge to the leaderships of both major political parties. 

“Their views are at odds with those of their own MPs. This promises to cause significant problems for both Theresa May and Jeremy Corbyn.

“The Prime Minister, in particular, might face considerable opposition from her own backbenchers when it comes to securing the kind of transitional deal she has indicated she wants.”