LONDON (Reuters) - Pro-Europe MPs’ efforts to temper Theresa May’s Brexit plan gained traction on Sunday when a member of her own party broke ranks to criticize her strategy before parliamentary votes that will test her government’s slim majority.

Britain's Prime Minister Theresa May leaves 10 Downing Street in London, Britain February 1, 2017. REUTERS/Neil Hall

A three-day debate on a law giving May the right to trigger Britain’s exit from the European Union begins on Monday, and will be followed by a series of votes on whether to attach extra conditions to her plan to start talks by March 31.

MPs voted overwhelmingly in favor of the principle of the new law last week, signaling May is unlikely to be blocked outright from triggering Brexit. But, she will need the support of her whole party to approve the strategy without change.

Sunday brought the first signs of internal Conservative Party dissent which, if they spread, could see the law amended, damaging May’s authority domestically and potentially giving EU negotiators a powerful lever in the exit talks.

“We could be faced with the prospect of leaving the EU by ‘falling off a cliff’ – as some have described leaving with no deal – with potentially disastrous economic consequences,” MP Neil Carmichael said on Sunday.

May has said parliament will be given a choice between accepting the deal she has reached with the EU, or rejecting it and leaving the bloc without any agreement on issues such as trade and immigration. But, MPs want to be given more influence.

“Parliament must have a final say when we get to the end-game,” Carmichael wrote in the Mail on Sunday, arguing that MPs should be able to send May back to the negotiating table.

Carmichael is the most outspoken of a handful of critics within May’s party who could join forces with opposition MPs from the Labour Party and the Scottish National Party to defeat the government.

May has a 16-seat working majority, but the actual number of rebels needed to inflict defeat could be higher depending on how smaller parties and pro-Brexit Labour MPs vote. One source said upwards of 20 Conservative votes might be needed to defeat her.

Pro-Brexit MPs were keen to head off the threat of a revolt.

“Any vote to amend this simple bill is a vote against the implementation of the referendum result,” said Conservative Euroskeptic MP Steve Baker.

Baker said there were as many 27 rebels in waiting. A source familiar with the cross-party talks said that number was higher than their own estimates. So far only Carmichael and one other MP, Anna Soubry, have publicly suggested they might vote against the government.