The government has already promised parliament a vote on the final deal, but believes restricting Ms. May's ability to leave the negotiating table could encourage the E.U. to offer a bad deal in the hope that lawmakers would then reject it and potentially halt Brexit.

“This amendment simply makes the negotiations much harder from day one for the prime minister as it increases the incentive for the European Union to offer nothing but a bad deal,” said George Bridges, the government's Brexit minister for the Lords, in his final plea before the vote.

Ms. May has insisted that she would be prepared to leave the E.U. without any deal if the terms on offer weren't good enough, stating in January that “No deal for Britain is better than a bad deal for Britain.”