Women have been pushed into sex work following the rollout of universal credit, an MP has said during a parliamentary debate on the controversial welfare reform.

Frank Field, chair of the Work and Pensions Committee, told the House of Commons on Monday that women in his constituency, Birkenhead, had resorted to prostitution for the first time in their lives after being left destitute by the new system.

Addressing work and pensions secretary Esther McVey, the independent MP said: “I wrote to the secretary of state about how the rollout of universal credit in Birkenhead is not going as well as we’re told in the House of Commons, with some women taking to the red light district for the first time.

“Might she come to Birkenhead and meet those women’s organisations and the police who are worried about women’s security being pushed into this position?”

In response, Ms McVey said the government needed to “work with those ladies and see what help we can give them from the work coaches, right the way through to the various charities and organisations”.

She then suggested that “in the meantime”, Mr Field could “tell these ladies that now we’ve got record job vacancies – 830,000 and perhaps there are other jobs on offer”.

It comes amid mounting pressure on Downing Street to rethink the highly contentious rollout of universal credit.

Chancellor Philip Hammond was warned last week that Tory rebels would defeat the government unless cuts for people moving onto the new system were stopped.

Conservative MP Heidi Allen said up to 30 Conservative backbenchers were ready to act unless the hardest-hit groups – single parents and second earners in families – were given urgent help.

Days before, former Conservative prime minister Sir John Major warned that Theresa May could face a backlash over universal credit similar to that experienced by Margaret Thatcher with the poll tax.

Heidi Allen: Conservative rebels will defeat government unless huge cuts for people moving onto universal credit are stopped

Sir John, who became Tory leader nine months after rioting broke out over the community charge in 1990, urged the government to rethink the rollout of its flagship welfare programme after reports it could leave families hundreds of pounds worse off.

Gordon Brown issued a similar warning on Tuesday, describing the reforms as “cruel and vindictive”.

Universal credit combines six means-tested benefits and tax credits into one payment and is designed to encourage people to take up work by ensuring they will always be better off having a job.