Theresa May is putting together a package of measures aimed at wooing Labour MPs in leave-supporting constituencies, offering greater protection for workers’ rights after Brexit and, it emerged on Wednesday night, cash for former coalfield communities.

The prime minister has asked two cabinet ministers to consult opposition backbenchers over legislation to protect workers’ rights after Brexit, although there is a fierce debate in Labour about how far to engage with the Conservatives.

Downing Street also confirmed that extra cash for deprived post-industrial areas was also under consideration, to allow “Labour MPs representing Brexit communities to say they have extracted something tangible”, according to a government source quoted in the Times.

As part of the charm offensive, Steve Barclay, the Brexit secretary, and Greg Clark, the business secretary, met Labour MP Melanie Onn on Wednesday to discuss further safeguards on workers’ rights.

The two ministers have also been tasked with drawing up proposals for enhanced environmental protections after Brexit showing how broadly May is willing to act in her efforts to persuade leave-supporting Labour MPs into voting for a revised Brexit deal.

Downing Street advisers pointed to remarks made by the prime minister during Tuesday’s Brexit debate, where she said: “The government will not allow the UK leaving the EU to result in any lowering of standards in relation to employment, ​environmental protection or health and safety.”

May had also told the Commons she wanted parliament to be able to “consider any measure approved by EU institutions that strengthens any of those protections” after Brexit in a calculated bid to win over some Labour MPs.

Downing Street hopes to persuade a handful of pro-Brexit Labour MPs to support any final deal that May brings back to parliament, partly because it needs to offset a group of diehard Conservative MPs that will not support any deal with the EU.

Onn, who described her meeting as positive, was one of 24 Labour MPs who rebelled against the party whip on Tuesday night, either by voting against or abstaining on Yvette Cooper’s amendment aiming to delay article 50 to buy time to prevent a no-deal Brexit.

In 2017, the Great Grimsby MP had proposed a bill that would transpose all workers’ rights protected under EU law into UK law post-Brexit after concerns were raised that some could otherwise be removed by a future government using only a statutory instrument.

This applies in particular to rights stemming from case law coming via the European court of justice, such as those applying to equal pay for part-time workers.

TUC officials are due to meet civil servants who are supporting the Barclay-Clark initiative on Thursday but there also remains considerable scepticism within the union movement about what is on offer.

A TUC spokesperson said: “Working people need a Brexit deal that provides a binding guarantee for existing rights and ensures that UK rights will keep pace with those across Europe into the future.”

The TUC added that the best way to do that would be to stick to “single market and customs union rules” – something that May has repeatedly refused to do.

Fourteen MPs voted against Cooper, including the former minister Caroline Flint and the MP for Crewe and Nantwich, Laura Smith, as well as veteran Eurosceptics Kate Hoey, Graham Stringer and Dennis Skinner.

The 10 MPs who abstained included the junior shadow ministers Gloria De Piero and Melanie Onn, as well as Tracy Brabin, Judith Cummins, Yvonne Fovargue, Mike Kane, Emma Lewell-Buck, Jim McMahon, Ruth Smeeth and John Spellar.

Chuka Umunna, a remain-supporting Labour backbencher, said he was “deeply disappointed” by the defeat of the Cooper amendment, as well as a bid by former attorney general Dominic Grieve to stage a series of votes on alternative Brexit plans.

“A no-deal Brexit would be a disaster for the jobs and livelihoods for people across the UK, and these votes have robbed parliament of the wide canvas needed to prevent that,” MP added.

Anti-Brexit MPs expressed disappointment at the size of the rebellion, saying it had strengthened the prime minister’s hand in showing that there was not a united front opposed to her. “What’s the point of Tories coming across if we can’t keep our side together?” one MP asked.

Labour indicated there would be little meaningful sanction against those who defied the party whip over Cooper’s amendment on Tuesday night. A party spokesman said they would be “spoken to by the whips’ office in the next few days”.