A £1.6 billion package promised by Theresa May for run-down towns has been dismissed by opposition MPs as a “pathetic” attempt to win Labour support for her Brexit deal.

The money, which will be spread over seven financial years to 2025-2026, is a “desperate bribe”, shadow chancellor John McDonnell claimed.

But Communities Secretary James Brokenshire said the money would be “transformative” and was not conditional on support for the Prime Minister’s Withdrawal Agreement.

And Mrs May’s official spokesman confirmed the money was not conditional on MPs backing the Brexit deal, telling reporters it was “absolutely not” a bribe in return for votes.

Downing Street confirmed that Attorney General Geoffrey Cox and Brexit Secretary Stephen Barclay will return to Brussels on Tuesday to continue their efforts to secure legally-binding changes to ensure that the UK is not trapped permanently by backstop arrangements designed to keep the Irish border open.

But Mrs May’s spokesman declined to discuss reports that Mr Cox has dropped attempts to secure a time limit for the backstop or a unilateral exit mechanism, telling reporters: “We are now at a particularly critical stage in these negotiations. I’m not going to get into specifics.”

The spokesman said the UK was “definitely making progress” after discussions spanning the past two weeks with the European Commission, he said.

But he added: “There definitely remains more work to be done.”

Mr Cox appeared to dismiss the reports, however, tweeting: “The DT (Daily Telegraph) reporting of the last 24 hours consists of misunderstood fag ends dressed up as facts.

“Some of it is accurate, much more of it isn’t and what is not is far more significant than what is.

“Complex and detailed negotiations cannot be conducted in public.”

The DUP and the Tory European Research Group (ERG) have made it clear they will not support the PM’s Withdrawal Agreement in crunch Commons votes without such legally binding measures.

Launching the new £1.6 billion Stronger Towns Fund package, Mrs May said: “For too long in our country 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.

“These towns have a glorious heritage, huge potential and, with the right help, a bright future ahead of them.”

Mr McDonnell branded the initiative a “desperate bribe”.

He said: “This Towns Fund smacks of desperation from a Government reduced to bribing MPs to vote for their damaging flagship Brexit legislation.”

But Mr Brokenshire told BBC Radio 4’s Today programme that the money was not linked to getting the deal through.

“This funding is there regardless of the outcome, but obviously we want to see a deal happening, we believe that is what is in the best interests of our country.

“But there is no constitutionality in that sense.”

Labour MP for Stoke Central Gareth Snell said: “The entire allocation for the West Midlands over four years is less than the total value of cuts faced by Stoke-on-Trent City Council alone over the same period.”

Luke Pollard, who represents Plymouth Sutton and Devonport, scorned the £35 million earmarked for towns in the South West, pointing out that it was around the same amount as the settlement agreed with Eurotunnel over the Brexit ferries “shambles”, adding: “What a pathetic mess.”

Rhondda MP Chris Bryant said the money – for English regions – was “corrupt, patronising, pathetic” and “all to appease the Brexit monster”.

Of the £1 billion being allocated using a needs-based formula, the North West gets £281 million, the West Midlands £212 million, Yorkshire and the Humber £197 million, the East Midlands £110 million, the North East £105 million, the South East £37 million, the South West £35 million, and the East of England £25 million.

Another £600 million will be available through a bidding process to communities in any part of the country.

Asked about the Daily Telegraph report, Mr Brokenshire said: “The Attorney General continues with his work to ensure that we get legally binding changes to ensure that we are not locked in the backstop.”

He said Mr Cox would be “back to Brussels this week to continue the discussions to make sure that we can get those legal changes”.

The Attorney General is reported to be focusing on securing an enhanced “arbitration mechanism” that allows the UK or the EU to provide formal notice that the backstop should come to an end.

But Brussels is said to be resisting demands for an “independent” arbitration panel, outside the jurisdiction of the European Court of Justice.

The ERG has set out three tests by which a “star chamber” of eight legally-trained Brexiteers will judge Mr Cox’s efforts to secure changes to the backstop.

The group wants a legally binding, treaty level arrangement; the language must not just simply reiterate the temporary nature of the backstop; and there “needs to be a clear and unconditional route out” of the arrangement.

DUP Westminster leader Nigel Dodds said his party must see legally binding and treaty-level changes to the Withdrawal Agreement regarding the backstop in order to support it.

He told BBC Radio 4’s Westminster Hour: “We need something which, whatever its legal form, has legal binding effect and which changes the current meaning of the Withdrawal Agreement.

“And which makes clear that it cannot be indefinite, and it cannot be a trap both for the United Kingdom generally and for Northern Ireland in particular.”

David Hughes and Shaun Connolly, Press Association Political Staff.