The opposition motion, backed by 155 votes to 69 - a majority of 86 - also called on May to rule out a no-deal split with Brussels.

It comes less than 24 hours before further key Brexit votes in the Commons.

The vote came at the end of a lengthy debate in the House of Lords on ongoing divorce talks with the EU.

Brexit Minister Lord Callanan argued the Labour motion, supported by the Liberal Democrats, sought "to tie the Government's hands in negotiations".

"We cannot support a motion which mentions 'all steps necessary' to avoid a no-deal, without excluding no Brexit from the list of necessary steps," he said.

He said a further vote would be brought forward by the Government, but disagreed with the "timing structures" proposed in the motion.

Opening the debate earlier, the Minister said it was reasonable to seek legally binding changes to the deal to reflect the "temporary nature" of the Northern Ireland backstop.

But Labour's leader in the Lords, Baroness Smith of Basildon, urged the Government to "stop dragging its feet, commit to asking for more time, and rule out the most disastrous of all outcomes - a no-deal Brexit".

Accusing Mrs May of trying to "run down the clock" and force a decision between her deal and no-deal, Lady Smith told peers: "It is only by securing a binding vote for MPs that they can apply the brakes before we career over a cliff-edge."

Lord Newby, Liberal Democrat leader in the Lords, branded the Government's approach "irresponsible" and warned the true economic costs of Brexit were now beginning to emerge with investment down and "anaemic" growth.

Lord Hope of Craighead, convener of the independent crossbench peers, said time was too short to put all the pre-Brexit legislation through Parliament and exit day must be postponed.

"Insisting that we leave on March 29 looks more and more absurd given that there is such a powerful case against a no-deal Brexit," he said.

Australian Associated Press