LONDON - Prime Minister Theresa May will travel to Northern Ireland and Wales on Tuesday as part of a tour of the United Kingdom designed to rally support for her widely criticised Brexit deal before a vote in parliament.

May secured agreement with the EU on Sunday for a deal that will see Britain leaving the bloc with continued close trade ties, but the odds now look stacked against her getting it approved by a deeply divided British parliament. 

Tuesday's tour includes meetings with political leaders from all parties in Northern Ireland - which will have Britain's only land border with the European Union and whose future has been a stumbling block in the negotiations.

"Having been told by the EU that we would need to split the UK in two, we are leaving as one United Kingdom," May said in a statement announcing the visit and defending the border arrangements agreed with the EU.

"My deal delivers for every corner of the UK and I will work hard to strengthen the bonds that unite us as we look ahead to our future outside of the EU."

The visit is part one of several fronts May's team are working on to build support ahead of the Dec. 11 vote in parliament. Some of her senior ministers have been praising the deal in public, and courting opposition lawmakers in private.

So far, the deal has failed to impress the Northern Irish Democratic Unionist Party (DUP) which props up May's minority government. The DUP said they would vote against the current form of the deal, drastically reducing May's chances of passing it, because it could leave the Northern Ireland subject to different rules than the rest of the country. 

May will highlight the business case for backing her deal, saying that it has support from manufacturers who "need to be able to trade freely across the border with Ireland and have unfettered access to the rest of the United Kingdom’s market".

May will also meet students, academics, and community and religious leaders in Northern Ireland. On the Welsh leg of the visit she will meet political leaders and farmers.

(Reporting by William James; Editing by Angus MacSwan) ((william.james@thomsonreuters.com; +44 207 542 3374; Reuters Messaging: william.james.thomsonreuters.com@reuters.net))