“It is clear that some in the Lords would seek to frustrate that process, and it is the government's intention to ensure that does not happen,” he said in a statement.

The defeat, however, could present a major headache for Ms. May if members of her own party follow through on their threats to rebel by supporting the amendment.

“I will vote to keep in this amendment,” Anna Soubry, a Conservative lawmaker in the lower chamber, told Sky News. She said parliament needed a proper say on the issue, warning of the dangers of a 'Hard Brexit' scenario where Britain left the E.U. without a deal.

A split within Ms. May's Conservative party would undermine her authority at a time when she is facing down demands for a second independence referendum from Scottish nationalists, managing fears that Brexit could destabilise Northern Ireland, and trying to persuade major EU powers they