Labour and leading trade unions have said they are unlikely to endorse any proposals from Theresa May aimed at improving workers’ rights after Brexit, with one leading figure accusing the prime minister of trying to “divide and rule”.

Trade unions involved in discussing a possible workers’ rights package, which the government hopes will help some Labour MPs support its Brexit deal, said they had yet to see anything from ministers they could support.

Union sources said they would want to see the government commit to putting future protection for workers’ rights in the Brexit agreement struck with the European Union, rather than in UK legislation that could be repealed by a future government.

They said May had shown no sign of taking on board their concerns about existing labour market regulation, under which, according to one official, an average UK employer “can expect a visit from an enforcement agency once every 500 years”.

The prime minister met several union leaders last week, including Len McCluskey, the Unite general secretary who is a key supporter of Jeremy Corbyn; the Unison leader, Dave Prentis; and Frances O’Grady, who heads the TUC. Union officials held meetings with civil servants on Thursday.

Greg Clark, the business secretary, and Steve Barclay, the Brexit secretary, are working on legislation that unions believe would commit the government to not lowering standards on employment, environmental protection and health and safety after Brexit.

As well as demanding that such protections are inserted into the exit treaty, unions want a binding commitment that the UK will match any improvements passed by the EU. So far, the government has said only that parliament would be able to vote on whether such improvements should be matched.

The ministers have also been talking to Labour backbenchers in leave-supporting areas, including John Mann, in the hope of getting at least a dozen to back May’s deal and make up for the lost votes of Tory Brexiters who will not support any deal May strikes with the EU.

The talks have included the idea of creating a “transformation fund” which could be invested in mining communities and other post-industrial, leave-supporting areas to support job creation, according to Mann.

Ian Lavery, Labour’s chair, said backbenchers should be careful about talking to the government, and that the prime minister was trying “the last move in the well-thumbed Tory playbook: divide and rule”.

“Any Labour MP seriously considering discussions with the PM should remember her record and that of her party going back generations. Quite simply, taking such a bribe would be fool’s gold,” he wrote in an article for Labour List.

Downing Street indicated on Friday that any transformation fund would not only cover areas represented by Labour MPs and would take in other deprived areas, such as fishing and other coastal towns.

The prime minister’s spokesman declined to give any details about the plans, but said any such initiative would cover “every part of the country” that needed investment, not just mining areas.

May spent Friday in her Maidenhead constituency as she continues to work on alternative proposals to resolve the Brexit impasse.

She is examining three options to deal with the unpopular Irish backstop, which is aimed at keeping the border open in case no long-term trade deal can be agreed. They are a time limit, a unilateral exit mechanism and alternative technological arrangements put to her by Tory backbenchers last week.

Her spokesman said May had no immediate plans to restart negotiations, or travel to Brussels, partly because Downing Street’s strategy continues to be to hope that EU leaders will reflect on her call to reopen the withdrawal agreement to remove the backstop, which the EU says is integral to a deal.

It is not clear when May will be able to present her revised Brexit plan. If she fails to do so by 13 February, she must make a statement before parliament and invite MPs to vote the following day on what they would like to see happen.