Andy Burnham said Britain had not voted for a hard Brexit as he repeatedly refused to rule out a referendum on rejoining the EU.

The Prime Minister said he would not “defend the deal” struck by the Tories, arguing that it had not lived up to what the country was promised in 2016.

His remarks, at Prime Minister’s Questions (PMQs) in the Commons, came after he suggested he could reinstate freedom of movement with the EU after the next election.

The Prime Minister’s words will heighten fears among Opposition MPs that he is attempting to delegitimise the Brexit vote. Earlier this month, he claimed that Russia had “clearly” interfered in the 2016 Brexit referendum.

“Hard Brexit” was a phrase coined during the negotiations to describe the then Tory government’s pursuit of a free trade agreement with Brussels.

It involved leaving the EU’s single market and customs union, ending free movement of people and the jurisdiction of the European Court of Justice.

In contrast, some Europhiles campaigned for a soft Brexit, which would have kept the UK much closer to the EU and following its rules.

At PMQs on Wednesday, Kemi Badenoch, the Tory leader, attacked the Prime Minister’s remarks on free movement, accusing him of having “opened his mouth without engaging his brain”.

The Prime Minister dismissed her suggestion that he had caused confusion over Labour’s position on Brexit, and denied reports of a Cabinet split.

He insisted the red lines in the party’s manifesto – which rule out the single market, customs union and free movement – would remain until the next election.

But he added: “What I won’t do is defend the deal negotiated, which in my view gave us a harder Brexit than was promised at the referendum and has been bad for growth and bad for control of immigration.”

Mr Burnham blamed Brexit for unleashing the “Boriswave”of immigration and accused the Conservatives of having left the EU “without a plan in place to control migration”.

He said an EU-UK summit next month would be “an opportunity to improve the poor deal that they negotiated and to get a better deal in place for Britain”.

At that gathering, the Prime Minister is expected to sign agreements to forge closer ties with Brussels on agricultural exports, carbon border taxes and electricity trading, which will all involve Britain following some EU regulations.

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