International Trade Secretary Liam Fox sent a message to the prime minister that quitting a backstop arrangement, aimed at preventing a hard Irish border, should be a decision for the UK alone.
The UK’s withdrawal agreement is 95% complete, although negotiations are continuing with Brussels over the stumbling block of the Irish border issue.
Brexiteers fear, under a backstop arrangement seeking to maintain a frictionless trade border with the Republic of Ireland, the UK could be left permanently in an effective customs union with the EU after leaving the bloc.
This could curtail Dr Fox’s ability to sign independent trade deals after Brexit.
The Irish government has rejected suggestions the UK could be handed the unilateral right to terminate a backstop arrangement at a future date, as reportedly being pushed by some of Mrs May’s top ministers.
Earlier this week, the prime minister’s cabinet discussed a “review mechanism” for bringing the UK’s participation in a backstop deal to an end.
But, asked whether the option of the UK exiting a backstop arrangement could be left as a decision to be mutually-agreed with the EU and Dublin, Dr Fox disagreed.
“We have an instruction from our voters to leave the EU,” he said.
“That decision can’t be sub-contracted to somebody else. That needs to be an issue for a sovereign British government to determine.”
A backstop arrangement would come into force if a future EU-UK trade relationship fails to prevent a hard border on the island of Ireland.
Amid concerns about the UK’s ability to exit such a scenario, the prime minister has also come under pressure to publish legal advice on potential post-Brexit arrangements for Northern Ireland.
Speaking as he entered the Cabinet Office to view the already-completed parts of the UK’s EU divorce deal, Dr Fox said he would make a judgement on whether government advice should be made public after viewing the text.
But he appeared to urge Mrs May to make available the full legal assessment of Attorney General Geoffrey Cox QC to her cabinet.
“It’s going to be really important we feel that we have the fullest possible information to make a decision that will have profound consequences for the future of our country,” Dr Fox said.
Sky News understands Environment Secretary Michael Gove, a leading Brexiteer like Dr Fox, is also among those cabinet ministers wanting to view Mr Cox’s advice in full before giving their consent to a deal.