Dusk falls over Parliament Square outside the Supreme Court after the third day of the challenge against a court ruling that Theresa May's government requires parliamentary approval to start the process of leaving the European Union, in central London, Britain December 7, 2016. REUTERS/Peter Nicholls

By Elizabeth Piper and Kylie MacLellan

LONDON (Reuters) - MPs backed Prime Minister Theresa May's Brexit timetable on Wednesday after she headed off a rebellion in her Conservative Party over a lack of insight into the government's strategy to leave the European Union.

May has come under pressure from MPs, businesses and investors to set out at least a broad picture of how she sees Britain's future relationship with the EU. She says giving too much away could weaken Britain's hand in the country's most important negotiations since World War Two.

After a sometimes rowdy session in parliament, MPs voted by 448 to 75 to support a motion calling on the government to offer up its Brexit plan, but also backed the government's timetable to trigger the divorce procedure by the end of March.

During the six-hour debate, the Labour Party pressed its motion for a plan setting out the government's negotiating stance in its talks with the bloc, before Article 50 of the EU's Lisbon Treaty is invoked to start the exit process.

But by agreeing to the government's demand for parliament to endorse May's timetable for Article 50, Labour MPs were accused of falling into a trap -- allowing ministers to begin the divorce without consultation.

Labour Brexit spokesman Keir Starmer denied the vote was on Article 50. It was a vote, he said, to force the government to offer a plan with "enough detail and clarity to end the circus of uncertainty" over Britain's future ties to the EU's single market of 500 million consumers.

"Asking for a plan setting out the objectives is not to seek to undermine the UK's negotiating hand nor is it to seek a running commentary, but it is in fact to have clarity, scrutiny and accountability," he said.

He said that if the government failed to provide a sufficiently detailed plan, Labour would challenge it again, he said, adding that the party aimed to head off a "hard Brexit".

The answer from government was clear -- it was offering information when it could and it would produce a plan. What was not clear was what would be included in that plan.

"I will make as much information as possible available without prejudicing our negotiating position," said David Davis, May's Brexit minister.

May hopes to stick to her timetable but faces obstacles after a court ruled that the government needs parliament's assent to invoke Article 50. The government is challenging that ruling in the Supreme Court.

A lawyer at the court said that even if parliament did vote in favour of the March deadline, that would make no difference to his case that parliament, not ministers, had the power to authorise triggering Brexit talks.

(editing by Angus MacSwan)