The group also wants attorney general Geoffrey Cox to rewrite official legal advice that says the backstop would "endure indefinitely" if no other way is found to keep a soft border in Ireland. It can't be a reinterpretation of the withdrawal agreement or a re-emphasis; it's got to be really clear language as to where we are going ...
British lawmakers oppose the backstop because it requires Britain to apply some European Union rules in Northern Ireland indefinitely, unless another plan for keeping the border open can be agreed in future.
Cox visited Brussels on Tuesday to discuss the hoped for "legally-binding" changes to the Irish backstop demanded by Brexiters.
"We will not, however, comment on the specifics of negotiations at this critical stage".
She added that, for "too long", prosperity has been "unfairly spread".
"Communities across the country voted for Brexit as an expression of their desire to see change-that must be a change for the better, with more opportunity and greater control", May said in a statement.
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She said: "After decades of neglect a one-off payment created to help the Prime Minister ahead of a key Brexit vote will fail, and it will confirm to people in our towns that the government is not serious in its commitment to our communities".
Responding on social media, Mr McDonnell said: "This Towns Fund smacks of desperation from a Government reduced to bribing MPs to vote for their damaging flagship Brexit legislation".
Rhondda MP Chris Bryant said the money - for English regions - was "corrupt, patronising, pathetic" and "all to appease the Brexit monster".
"Voters will not be fooled - especially lose in areas which voted leave and are now demanding a People's Vote because they know, whichever way you do it, Brexit will harm their futures".
The "Stronger Towns Fund", details of which appeared in newspapers last month, is seen by many as part of May's efforts to win support for her Brexit deal from opposition Labour lawmakers who represent areas, particularly in northern England that voted strongly in favour of leaving the European Union.
Most of the initial one billion pounds will go to communities in the English north and Midlands, where many Labour-held parliamentary constituencies returned a majority for Brexit in the 2016 referendum.
But the TUC said legally-binding commitments on workers' rights were missing from the withdrawal agreement and the best way for the United Kingdom to maintain existing standards was to remain in the EU single market and some form of customs union - which No 10 has rejected.
"And which makes clear that it can not be indefinite, and it can not be a trap both for the United Kingdom generally and for Northern Ireland in particular".