LONDON (REUTERS) - Prime Minister Theresa May will not accept a proposal to hand Parliament more control over Brexit, a source said on Tuesday (June 19), setting up a showdown with lawmakers who want to prevent Britain from crashing out of the European Union without a deal.

Mrs May has struggled to get backing for her plans to cut ties with the EU, forced to find a compromise last week with pro-EU lawmakers in her Conservative Party to try to get their backing for her Brexit blueprint, or the EU withdrawal Bill.

Her compromise failed, and on Wednesday she will again try to head off a rebellion over the so-called meaningful vote on any Brexit deal that some lawmakers want to be able to make sure the government cannot accept a "no deal" with Brussels.

The government source said on condition of anonymity that Mrs May would stick to her proposal to offer lawmakers a vote on a statement outlining the next steps if she fails to win agreement with the EU, or if Parliament rejects any deal she comes up with.

"We won't be accepting the Lords amendment," the source said, referring to a decision in the Upper House of Parliament on Monday to again try to force the government to hand the House of Commons more control over Britain's exit from the EU.

The pro-EU Conservative lawmaker, Mr Dominic Grieve, who has led efforts to hand Parliament a greater say, said he was still looking forward to having discussions with the government to find a way out of a row that has questioned Mrs May's authority.

"It has been suggested that I want to collapse the government - I don't," Mr Grieve told BBC Radio.

He said he did not want Britain to leave the EU without a deal but that the government had to be prepared for that outcome.

"If we have no deal at the end, it is a very serious crisis," he said.