Theresa May is to formally announce a series of new pledges on workers’ rights and the easing of trade union restrictions, in the latest attempt to get Labour MPs to support her Brexit deal.

Labour sources said they were expecting the prime minister to table a ministerial statement next week setting out greater guarantees for workers post-Brexit, including a “non-regression lock” and giving MPs a vote on whether to adopt future EU rules on workers’ rights.

It was also set to include a reporting mechanism to involve trade unions and the Confederation of British Industry when the government considers such adoptions. MPs would be able to amend votes on future EU workers’ rights legislation, meaning they can potentially force the government to accept new rules.

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Unions, including Unite, were expected to be consulted in the final stages of preparing the statement, though the TUC’s general secretary, Frances O’Grady, has been publicly sceptical about the guarantees.

It is unclear whether the final package of measures will be offered as a separate bill, which some Labour MPs have demanded, or as part of the EU withdrawal bill, which other Labour MPs prefer because they believe it would be harder to unpick.

Labour MPs who support the new measures are unsure how many more colleagues will be won over by them. “I don’t know how many more people’s minds this is going to shift,” one said.

A Downing Street source said the timing of the announcement had not been finalised, though it would be before the meaningful vote. The prime minister may hold the vote next week, before the 12 March deadline, depending on when the attorney general, Geoffrey Cox, is able to reach an agreement with Brussels.

In her statement to the Commons on Tuesday, May promised to give parliament a vote on whether it wished to follow EU standards in areas such as workers’ rights and health and safety. She also pledged that the government would consult with businesses and trade unions when it looked at new EU legislation.

The prime minister promised to give the commitments force in UK law, without specifying the form this would take.

May has been talking to a small group of Labour MPs who have been pushing for the guarantees, including the former minister Caroline Flint and the backbenchers John Mann and Gareth Snell.

Snell robustly defended the group’s actions in an exchange during the Brexit debate, saying: “I have spoken to the prime minister about workers’ rights, funding for our towns post-Brexit, and what we need to do to find a way through this. Some of my colleagues have labelled those things as bribes, but they are wrong; what we are trying to do is find a constructive way forward.”

James Brokenshire, the communities secretary, is expected to announced a £1.6bn Brexit fund, spread over seven years, for towns and coastal communities. Government sources said they hoped it would be announced before the next meaningful vote.

The fund was intended for 26 of the 38 “local enterprise partnerships” and none of it would go to London. Regions such as the Black Country, Greater Manchester and other Midlands regions, for example, Nottinghamshire and Derbyshire, were likely to get the most significant funding, according to the Sun.

May confirmed at prime minister’s questions on Wednesday that there would be a fund to “ensure our towns can grow and prosper”, but declined to give further details.