In her letter, May urged Britons to start new era of political unity when it leaves EU on March 29, 2019.
London: Prime Minister Theresa May made a dramatic direct appeal to the British public to support her deal to exit the European Union on Sunday even as backing from her own party for the agreement appeared to elude her.
May is meeting the other 27 EU leaders in Brussels this weekend to sign off on a divorce treaty and political declaration to end more than 40 years as part of the world's biggest trading bloc.
In an open letter to the nation, May said she would campaign "heart and soul" to get her Brexit deal through Britain's parliament - an increasingly unlikely prospect given stiff opposition from some of her own Conservative Party lawmakers and allies in Northern Ireland's Democratic Unionist Party (DUP) alike.
"It will be a deal that is in our national interest - one that works for our whole country and all of our people, whether you voted "Leave" or "Remain," she said.
Sunday newspapers said different factions in her own party were preparing alternative Brexit plans to keep Britain closer to the EU should her deal fail as most expect.
That included a plan being hatched by close allies such as finance minister Philip Hammond and work and pensions minister Amber Rudd, reported The Sunday Times without citing sources.
The Sunday Telegraph said there were plans on both sides of the English Channel for a "Plan B". One such was a Norway-style relationship with Brussels, under which Britain would have a more certain "exit mechanism" from the EU's rules but would be unable to end the free movement of workers from the bloc - the most politically contentious element of Brexit.
In her letter, May urged Britons to start a new era of political unity when it leaves the EU on March 29, 2019 and set aside the bitter fighting provoked by Brexit.
"I want that to be a moment of renewal and reconciliation for our whole country. It must mark the point when we put aside the labels of "Leave" and "Remain" for good and we come together again as one people," she said.
"Parliament will have the chance to do that in a few weeks' time when it has a meaningful vote on the deal."