London - British MPs have voted to give themselves a bigger say in what happens if, as expected, Prime Minister Theresa May's Brexit deal is rejected by the House of Commons next week.

Here is what happened and the possible impact it could have on Britain's withdrawal from the European Union next March.

- What happened?

During a procedural discussion at the start of the debate on the Brexit deal on Tuesday evening, a number of MPs from May's Conservative party tabled an amendment seeking to influence what happens if that deal is rejected in a vote on Tuesday next week.

The amendment, backed by former attorney general Dominic Grieve among others but opposed by the government, was passed in the House of Commons by 321 votes to 299.

Pro and anti-Brexit demonstrators outside Parliament

- What does it say?

If the Brexit deal is rejected, the government must return to the Commons within 21 days to make a statement on what happens next.

The Grieve amendment removes the requirement that any motion arising from this statement be considered "in neutral terms" -- essentially, it allows MPs to amend it.

- What impact could this have?

Former minister Oliver Letwin, who backed the Grieve amendment, said the priority was to avoid the potentially calamitous situation of Britain leaving the EU with no deal.

"It could be that at that time there is somewhere across this House a majority in favour of some solution that would avoid us leaving without a deal," he told the debate.

MPs could in theory table an amendment asking the government to reopen negotiations with the EU or demand a second referendum or seek to delay Brexit or perhaps even try to stop it altogether.

Letwin said he backed May's deal but if that failed, suggested a Norway-style agreement, where Britain joins the European Economic Area (EEA) -- an option several Conservative MPs are pushing.

Brexit explained in 9 graphics

- Can MPs stop Brexit?

MPs are sharply divided over the various possible versions of Brexit, and both the Conservatives and Labour have committed to leaving the EU.

However, everything might change if May's deal is taken off the table.

Brexit supporters say any direction the Commons gives the government would not be legally binding.

Some suspect dirty tricks, noting the Conservative rebels who backed Grieve's amendment include some of May's close allies.

The amendment's success reinforces the prime minister's previous warnings to eurosceptics that if they reject her deal, they risk having no Brexit altogether.

- A new government?

If the Brexit deal falls, May is also likely to face attempts on all sides to unseat her.

The Labour party says it would probably table a vote of confidence in the House of Commons.

Eurosceptics in her own Conservative party could also launch a fresh challenge against her leadership.

By Alice Ritchie