Labour is planning to team up with Conservative rebels to change the government’s key Brexit bill when it returns to the House of Commons.
The opposition wants to ensure the European Court of Justice still has a role during the transitional period planned after March 2019.
Its Brexit spokesman Keir Starmer claimed “very many” Tory MPs shared his concerns.
But the Conservatives hit back, saying Labour was “confused” on Brexit.
The EU Withdrawal Bill is crucial to the government’s strategy for leaving the EU. EU law that currently applies in the UK will be “cut and pasted” on to the UK’s statute book in an attempt to ensure a smooth transition on Brexit day.
The bill returns to the House of Commons on Tuesday when it faces hundreds of attempts by MPs to change its wording.
BBC political editor Laura Kuenssberg said the government “knows it’s going to have to compromise”, with concerns being raised about the draft legislation by MPs across all parties.
Setting out his party’s plans, Sir Keir said it was “crunch time” for the bill.
He said the legislation’s current wording prevented the European Court of Justice from having a role as the UK transitions to its final Brexit arrangements.
This would make it difficult to stay in organisations like the European Medicines Agency, he said.
Labour’s “very simple amendment” would “correct that flaw” he said, adding that his party was doing this “in the national interest”.
Asked if he was confident of getting the amendment through, Sir Keir said “there are very many Conservatives who are concerned about this”.
The government has vowed to end the jurisdiction of the European Court of Justice in the UK.
Sir Keir the long-term relationship with the ECJ was “a matter for negotiation” and that its jurisdiction “would have to change” but said making it a red line had been a mistake.
It was “blatantly obvious” that the final agreement would not be in place by March 2019 – when the UK leaves – he said, adding that this made the transition deal vital.
But Tory MP Chris Philp dismissed his claims, saying: “Labour are so confused on Brexit, they’ve set out 10 different policies on it since the EU referendum.
“Only the Conservatives have a plan that will ensure that a smooth and orderly Brexit sees our legal system functioning on day one – the only thing Labour policy would ensure is legal chaos.”
Ahead of the return of the EU bill, Brexit Secretary David Davis will update MPs on the progress of negotiations later on Monday.