Rishi Sunak was accused by the Labour party of being at the mercy of “malcontent” Tory MPs on Wednesday, as the prime minister’s efforts to land a Brexit deal on Northern Ireland hit further problems.

Sunak had hoped to present a deal to reform Northern Ireland’s trading rules by now, but his allies admit he has had to go back to Brussels to discuss ways to satisfy his critics.

The prime minister has told Northern Ireland’s Democratic Unionist party and Eurosceptic Tory MPs that he has secured a key deal to return control of VAT and state-aid rules from Brussels to Westminster.

But the DUP and Tory European Research Group, which are co-ordinating their tactics, want to see the legal detail before they welcome any agreement and in the meantime are increasing their demands.

Sir Jeffrey Donaldson, the DUP leader, told Sunak he did not want just a tweak of the Northern Ireland protocol, part of Boris Johnson’s 2019 Brexit deal, but wanted to rewrite “the legally binding treaty”.

EU member states insist they will not reopen the protocol but were willing to improve its implementation. “We can’t,” said one EU diplomat. “What we are doing is in the framework of the protocol and withdrawal agreement.”

Donaldson also said this week he wanted Sunak to create a dual regulatory regime in Northern Ireland, so that manufacturers in the region could choose to produce goods under UK rules for sale in the UK market only, rather than under EU single market rules.

The ERG is backing the DUP’s calls for a big overhaul of the protocol, the trade rules that leave Northern Ireland as part of the single market to avoid the creation of a hard border on the island of Ireland.

Sir Keir Starmer, Labour leader, told MPs: “It’s the same old story: the country has to wait while the prime minister plucks up the courage to take on the malcontents, the reckless and the wreckers on his own benches.”

Sir Simon Fraser, former head of the Foreign Office, tweeted: “How come Number 10 let Rishi Sunak get so exposed on Northern Ireland when there was so much heavy political lifting still to do?”

Sunak did not brief the DUP on his plan until the end of last week and brought the ERG into his confidence only this week, leaving some of his critics saying they were being “bounced” into accepting the outline agreement.

One veteran of Brexit negotiations said: “It’s incredible they left it this late. They should have started bringing the DUP on board weeks or months ago.”

The prime minister said parliament would be able to “express a view” on the deal but did not specify how exactly this would take place.

Sunak, who briefed Northern Ireland business leaders on Wednesday, has tried to allay concerns over the application of EU state aid and VAT rules to the region, saying they would in future be run from Westminster.

The development, first reported by Sky News and confirmed by DUP and Tory officials, would remove one of the irritations of the protocol from the point of view of pro-UK unionists.

But Sammy Wilson, DUP chief whip, said his party had seen “no details to assess if there are any exemptions”.

A senior Tory MP said: “On the face of it, it’s good news, but how will they actually deliver it?”

An EU official confirmed that the UK would have more freedom to set VAT, tax and state-aid rules in Northern Ireland but said there would be “strings attached”.

The prime minister also pledged to address the “democratic deficit” in the deal, giving the Stormont assembly a say over EU rules affecting the region and ensuring the European Court of Justice arbitrates only as a last resort.

Stephen Kelly, head of the industry group Manufacturing NI, said Sunak appeared to have “an intimate understanding” of the issues when he briefed business leaders on a video call on Wednesday.

But Kelly said he feared relations with the EU could sour if Sunak lost his nerve and retreated from the outline deal taking shape in the face of political opposition.

“I think there’s real jeopardy here, a risk of going back rather than going forward, unless this thing is done in the next number of days,” he said.