David Cameron is to face Labour claims in the Commons that he sold the country down the river at the EU summit by failing to protect vital national interests.

He will also face Tory backbench concern that he abandoned a vow to block the rest of the EU using European institutions such as the European court of justice to enforce its new fiscal pact. The pincer movement could be uncomfortable for the prime minister, who is due to make a statement about Monday's EU summit to the house on Tuesday afternoon, as his diplomatic tactics come under scrutiny.

The issue was also discussed at Tuesday morning's Cabinet meeting. The prime minister's official spokesman said there was "agreement round the Cabinet table" when Cameron reported back on the outcome of the summit.

He said the work and pensions secretary, Iain Duncan Smith, raised legal issues over the use of EU institutions, but recognised that they had been registered in the treaty.

The former Conservative minister for Europe David Davis told BBC Radio 4's World At One programme that he expected the Commons to be understanding.

"People will want to be helpful – nobody thinks that David is some sort of mad europhile – and they also understand that he has got the Liberal Democrat party to keep on board," the eurosceptic MP for Haltemprice and Howden said.

The prime minister's position "has actually got to mean that we reserve the right to veto something late on, whether it is the use of the court or whether it is some element of the treaty".

"I don't think the House will be hostile, I think it is just going to be worried that what it thought was a veto is turning into something else."

The Labour leader, Ed Miliband, speaking on ITV, said: "I'm very concerned about what David Cameron has done because he trumpeted last December that he got a great deal for Britain, he'd protected us and everything, and the way that Europe was going to go about this treaty … wasn't going to affect Britain. Now he seems to have sold us down the river on a lot of things so I'm going to be asking him in the House of Commons today what exactly has he agreed to, what protections has he got for Britain."

Miliband said it would have been better for Britain to stay at the table at the last summit rather than vetoing a treaty. "I say it's a phantom veto and, frankly, he's completely mishandled these negotiations."

Accusing Cameron of publicity-seeking opportunism, Miliband said the prime minister had failed to protect the interests of the City of London.

He said Cameron "went into those talks saying his real worry was about financial services and how that would be affected if other countries went ahead".

"He's secured no extra protections for financial services. The one claim he made was: 'Well, look, OK, I may not have secured any extra protections, but at least it's not a fully fledged European treaty, using those European institutions, with the weight of the commission, the court of justice, behind it … everything I'm reading and hearing suggests that that turns out not to be the case."

Tory MPs are blaming Cameron's actions on the excessive influence of the Liberal Democrats.