British Prime Minister Theresa May (Front) attends a debate on the Brexit deal amendments in the House of Commons in London, Britain, on Jan. 29, 2019. (Xinhua/UK Parliament/Mark Duffy)

LONDON, Jan. 29 (Xinhua) -- Just days after suffering the biggest humiliation in British political history, Prime Minister Theresa May was closer than ever Tuesday to finally reaching an elusive Brexit deal.

By 317 votes to 301, MPs in the House of Commons gave their backing to May's deal which they rejected earlier this month, providing changes are made to the so-called Irish backstop border issue.

The 16 majority for her deal gives May a mandate to return to Brussels to call for a re-opening of negotiations, and indicates that the Brexit deal is likely to win the critical final vote in British parliament if changes are made to the Irish border issue.

The victory for May's minority government was assured after the Democratic Unionist Party (DUP) backed tonight's move.

Immediately after the vote was announced, May said that two weeks ago MPs rejected the Brexit Withdrawal Agreement when only 202 MPs voted in favor.

"Tonight a majority have said they would support a deal with changes to the backstop.

"It is now clear that there is a route that can secure a substantial and sustainable majority to leave the EU with a deal," she said, to loud cheers from the Conservative benches.

Veteran MP Sir Graham Brady has been hailed as the hero of the night by including a crucial addition to May's rejected deal. It says the deal requires the Northern Ireland backstop to be replaced with alternative arrangements to avoid a hard border.

The words were enough to win over the DUP as well as Conservative politicians strongly against a backstop over fears it could tie Britain permanently to the EU.

May said the British government can look forward to obtaining legally binding changes to the withdrawal agreement with regards to the backstop, allowing no hard border between Ireland and Northern Ireland.

May and her senior advisers are not waving victory flags at the moment, with the developments in London receiving a frosty reaction in Brussels and Dublin.

May admitted that winning over Brussels will not be easy. She said: "With changes to the backstop, plus assurances on workers' rights, it is now clear there is a route to passing a deal."

May said there was limited appetite for such a change in the EU and negotiating it will not be easy. "But MPs have now made it clear what it wants," she said.

The Irish prime minister Leo Varadkar, said in a statement issued later in Dublin: "The withdrawal agreement is not open for re-negotiation."

Referring to the withdrawal agreement agreed between EU leaders and May, Varadkar said it is a carefully negotiated compromise, which balances the UK position on customs and the single market with avoiding a hard border and protecting the integrity of the EU customs union and single market.

He said Ireland will continue its preparations for all outcomes, including for a no-deal scenario.

A spokesman for Donald Tusk, president of the European Council, said: "The backstop is part of the withdrawal agreement and the withdrawal agreement is not open for re-negotiation."

The Labor leader Jeremy Corbyn, who earlier in the evening, lost a vote that would have avoided a no-deal outcome, said he was now prepared to meet May to discuss Brexit.

The business world reacted to May's victory in the House of Commons.

Adam Marshall, director general of the British Chambers of Commerce said another day had been lost while the clock is ticking. "Government and parliament are still going round in circles when businesses and the public urgently need answers," he said.

Stephen Martin, director general of the Institute of Directors said: "The prime minister clearly faces a difficult task in winning a compromise on the backstop. However, if the choice is between trying to change the deal and leaving without one, business will have to hope the EU can be flexible and consider whether any legal changes at all could further clarify that the backstop is not a permanent fixture."

May plans to discuss developments with the EU ahead of returning at a later date to the British Parliament for a meaningful date needed on a deal with Brussels.

Until now Brussels has insisted that a backstop must be part of the Brexit deal to avoid a hard border between EU member state Ireland, and Northern Ireland, which is part of the UK.

Britain is scheduled to leave the EU on March 29.