British Prime Minister Theresa May faces a day of reckoning on Monday as mutinous lawmakers try to trigger a no confidence vote over their opposition to her draft European Union divorce deal, a rebel member of her Conservative Party said.

"This is absolutely the day at which we stand at the bar of history on this," Simon Clarke told the BBC, adding "this day must be the point at which ... action is taken."

"If we continue with this plan we are simply not going to have a government because the clear threat it poses to the integrity of the union is something which our colleagues the DUP will simply put up with," he told BBC radio.

Clarke, who has submitted a letter of no confidence in the British leader, said every hour and every day that the Brexit deal was not rejected, was a day wasted on credible negotiations.

"It is quite clear to me that the captain is driving the ship at the rocks," he said.

The Sun Newspaper reported Monday that 42 Conservative Party lawmakers have said they would submit letters of no confidence in the prime minister.