Labour leader wants full access to EU markets for British firms but would seek to ditch certain directives and obligations

Jeremy Corbyn believes Britain should reject key aspects of the single market when it leaves the European Union, he has made clear, sparking a fresh row with some of his party’s MPs.

In a briefing after prime minister’s questions, a senior Labour source said Corbyn wanted to ditch some of the rules which other member countries see as integral parts of the single market – including restrictions on when governments can bail out failing companies.

“There’s a question about what ‘membership of the single market’ actually means,” the source said. “It’s often interpreted as the whole collection of treaties and directives around the four basic pillars of the EU: free trade in goods, services, labour and so on. There are aspects of that which Jeremy campaigned against in the referendum campaign.”

After a number of Labour MPs urged Corbyn to clarify his position, he released a personal statement. He said he would be “pressing for full access to the European single market” for Britain’s firms, but added: “There are directives and obligations linked to the single market, such as state aid rules and requirements to liberalise and privatise public services, which we would not want to see as part of a post-Brexit relationship.”

Labour sources insisted Corbyn’s position was consistent with shadow chancellor John McDonnell’s claim in the aftermath of the Brexit vote that “the damage that would be done to our economy by pulling out of the single market at this time could be substantial”.

But other EU member states may be unwilling to allow Britain to cherrypick the parts of single market membership they like, while rejecting some of its key rules.

The idea of having “access” to the single market, without remaining a member, has also been mooted by many pro-Brexit campaigners.

But the Brexit secretary, David Davis, was slapped down by the prime minister earlier this week for suggesting it was “improbable” Britain would remain a member.

Some Labour MPs were alarmed by Corbyn’s remarks, which they feared suggested he would be willing to accept a “hard Brexit” – involving leaving the single market – which some predict would severely damage the economy.

Leadership challenger Owen Smith, the MP for Pontypridd, said: “Jeremy seems happy to accept Brexit at any cost – even if that means putting British jobs and investment at risk.

“Perhaps this explains why he failed to ask a single question of Theresa May at prime minister’s questions about Brexit, and why he failed to campaign hard enough during the referendum.”

Scottish Labour leader Kezia Dugdale wrote to the first minister Nicola Sturgeon to stress that: “Scottish Labour is an autonomous party. We have repeatedly supported your efforts to meet with governments around the world to not only seek to find a way to retain our EU membership, but also to make clear that Scotland remains open for business.”

And prominent Labour backbencher Chuka Ummuna said: “Working people the length and breadth of Britain benefit enormously from Britain’s place in the European single market. Labour should be fighting for Britain to stay in the single market, not turning a blind eye to its advantages.”

Corbyn has long been a critic of the EU. His campaigning for Britain to remain a member was considered by some MPs to be lukewarm – a key factor in driving the mass resignations that followed the referendum result.

But his allies regard Brexit as an opportunity to free Britain from what Corbyn, in his response to a statement on Brexit from the prime minister, called “free market dogma”.

May seized on his words, suggesting Labour had turned away from free trade, styling post-Brexit Britain as a champion of globalisation.