LONDON, June 20 (Xinhua) -- British Prime Minister Theresa May won a crucial vote in the House of Commons Wednesday when MPs rejected a call by a former government official to give parliament a meaningful vote on a Brexit deal with Europe.

Conservative MP Dominic Grieve proposed that MPs should decide on a deal Britain makes with the European Union on the terms of their future relationship after Brexit.

In what was a nail-biting finale to several weeks of intense debates in both the House of Commons and the House of Lords, MPs by 319 votes to 303 rejected the proposal put forward by Grieve.

The success for May and her Brexit Secretary David Davis came after a last minute concession to revel MPs who had threatened to support Grieve. The result meant that MPs backed May over what would happen in the event of there being no deal with the European Union.

Later Grieve told the Guardian newspaper: "We've managed to reach a compromise without breaking the government - and I think some people don't realise we were getting quite close to that.

"I completely respect the view of my colleagues who disagree, but if we can compromise we can achieve more."

Meanwhile, Tom Brakes, Brexit spokesman for the minority Liberal Democrats accused the rebels of getting cold feet.

He said: "Despite the clear calamity that May and Davis are making of Brexit, the so-called Tory rebels have lost their bottle and caved into yet another pathetic government compromise that isn't worth the paper it is written on."

The Guardian reported that Grieve voted against his own amendment following the last minute government concession, but six Conservative MPs voted against the government in the vote.

The Brexit Withdrawal bill will now go back to the House of Lords where it is almost certain to be supported, paving the way for Royal Assent by Queen Elizabeth II.

But for May, the Brexit battles are not over, with other bills relating to Brexit waiting in the wings to be discussed by the Houses of Parliament.