Members of the Lords EU committee wrote the prime minister to warn that securing a trade deal must remain the "only priority" for David Frost, the UK's chief Brexit negotiator, after he was handed another top government job.
Mr Frost's surprise appointment following the departure of UK's top civil servant Sir Mark Sedwill sparked outrage over his lack of experience in national security matters and his political background.
Sir Mark will stand down as both national security adviser and as cabinet secretary in September following weeks of hostile newspaper briefings, widely believed to originate from Downing Street.
Mr Frost, an ally of the prime minister, will replace him in the national security role while continuing as the UK's chief Brexit negotiator - in a clear signal that No 10's focus is shifting away from the EU talks.
In a letter to the prime minister, committee chairman Lord Kinnoull said: "The EU is our closest neighbour and ally, and our biggest trading partner—it is difficult to over-state the importance of the UK-EU negotiations.
"It is thus critical that the negotiations should indeed remain Mr Frost’s “top priority”—in fact his only priority—until they are concluded, one way or another.
"Can you therefore confirm that Mr Frost will remain in post as the UK’s chief negotiator until the negotiations are completed and a final legal text is ready for ratification?"
Lord Kinnoull pointed to EU Brexit negotiator Michel Barnier's insistence that negotiations must continue into the autumn and questioned how Mr Frost would balance the heavy demands of both roles.
It comes as the first face-to-face trade talks with Brussels ended a day early, with the British team saying "significant differences" remain between both sides.
Both sides will meet again next week in London but clear divisions remain over issues such as fishing rights and EU regulations.
If a deal cannot be struck before the end of the transition period in December, the UK will crash out of the EU's single market and the customs union without any agreement on future access.