The Game of Thrones actor Kit Harington has called on people to sign a petition from the learning disability charity Mencap asking for the government to foot the estimated £400m bill faced by care charities in back pay for sleep-in shifts.

The online petition, which has attracted more than 7,000 signatures, says many care providers face bankruptcy because of the bill, which “could mean the end of social care as we know it”.

According to Mencap, sleep-ins are used widely in the learning disability sector to provide care for vulnerable adults, and until recently workers were paid a flat-rate, “on-call” allowance rather than the national minimum wage.

The flat rate is typically £35 to £45, with workers receiving either the national minimum wage or the national living wage for the hours they spend providing care.

But in the wake of two employment tribunal decisions from last year, the Department for Business, Energy and Industrial Strategy changed its guidance to ensure the national minimum wage applied to sleep-in carers.

As a result, HM Revenue & Customs has begun asking disability charities to give six years of back pay to affected staff. Mencap said this could cost the sector as much as £400m.

“We are asking the government to urgently commit to paying this bill as the sector cannot afford it,” the petition says. “Government caused this problem: only they can fix it.”

A statement last week from the Department for Business, Energy & Industrial Strategy said employers that underpaid workers for sleep-in shifts before 26 July 2017 would have historical financial penalties waived and HMRC would suspend its enforcement activity about sleep-in care shifts until 2 October.

“The government will continue to look at this issue extremely carefully alongside industry representatives to see whether any further support is needed and ensure that action taken to protect workers is fair and proportionate, while seeing how it might be possible to minimise any impact on social care provision,” the BEIS statement said.

“The learning disability sector in the UK is on the brink of crisis,” says Harington in the video. “It is faced with a back-pay bill of £400m which it cannot pay.

“Many of the providers of this essential, sleep-in service face bankruptcy. And some of the most vulnerable people in our society will be left without care, without hope and without an independent future.”

Harington, who is an ambassador for Mencap, has a cousin with Down’s syndrome and autism, who has been supported by the charity throughout her life.

Another Mencap ambassador, the DJ Jo Whiley, who has a disabled sister who receives sleep-in care, helped to launch the petition last week.

Jan Tregelles, chief executive of Mencap, said in a statement that the back-pay problem was the “most critical issue that Mencap has faced in 70 years”.