British Prime Minister Theresa May attends the Prime Minister's Questions in the House of Commons in London, Britain, Jan. 30, 2019. Multiple options for Brexit still remain a possibility after Theresa May was given the backing of the House of Commons to renegotiate her European Union Withdrawal Agreement. (Xinhua/British Parliament/Jessica Taylor)

BRUSSELS/LONDON, Jan. 31 (Xinhua) -- British Members of Parliament (MPs) signaled their support for Prime Minister Theresa May's revised Brexit deal, but the European Union (EU) said it won't consider it.

The Withdrawal Agreement between the EU and Britain remains the best and only deal possible and will not be renegotiated, said Jean-Claude Juncker, president of the European Commission, at the European Parliament's plenary session debate on Wednesday.

"The European Union said so in November. We said so in December. We said so after the first meaningful vote in the Commons in January," Juncker said, casting a cloud over Britain's latest move toward Brexit.

May was buoyed by a majority vote in the House of Commons on Tuesday night, backing her Brexit deal if the so-called Irish border stopgap measure is removed.

It puts her Brexit deal within grasp, if she can persuade EU leaders to agree to change their insistence on measures to prevent a hard border between Northern Ireland and the Republic of Ireland.

"MPs decided they want May and the EU to change the Irish Backstop," Alan Wager, fellow at the independent think-tank UK in a Changing Europe, told Xinhua in an exclusive interview.

"They say that leaves Britain tied too closely to the EU, and also following its rule; they want to make the UK less bound to EU rules," Wager said.

The Withdrawal Agreement contains a Northern Ireland Backstop, which seeks to preserve the open border between the two nations.

"What May's MPs want is something that says the EU and Britain are not locked into this agreement on the Northern Irish border indefinitely," Wager said.

Both Juncker and the EU's chief Brexit negotiator Michel Barnier, however, said that they would reject any British efforts to renegotiate the Irish border backstop.

"It looks like although May has now a majority in parliament, something she was lacking a couple of weeks ago, she now needs to go back to the EU and reopen those negotiations -- she will find it very difficult to get a compromise that will be supported by the EU and by her own MPs," Wager said.

London and Brussels have joined a game of chicken.

May plans a series of meetings starting Thursday with politicians from her Conservative Party to consolidate the support she received Tuesday night.

Britain is due to leave the EU on March 29.

May now has several weeks to persuade the EU to change its mind on the Irish backstop arrangement.