A powerful cross-party group of MPs today warns Theresa May that Brexit is “sucking the life” out of her government – as cabinet sources admit that the crisis is forcing vital domestic business off the government’s timetable.

With the deadlock over May’s Brexit deal unresolved, and a key vote in parliament postponed until mid-January, the chairpersons of six all-party select committees have signed a statement saying long-drawn-out arguments over Brexit are having a “serious detrimental effect” on wider domestic policy.

The MPs, who include the Tory chairs of the treasury and education select committees, Nicky Morgan and Robert Halfon, add that: “Rather than continuing to drag out the Brexit process for months more, we must bring it to a close if we are to prevent serious damage to our country”.

Others who signed off on the statement are the chair of the work and pensions select committee, Frank Field; the Tory chair of the digital culture media and sport committee, Damian Collins; the Labour chair of the environmental audit select committee, Mary Creagh; and Norman Lamb, the Liberal Democrat chair of the science and technology committee.

While the six have very different views on Brexit they agree that the government is letting people down with its near-total preoccupation with the issue at a time of crisis in the NHS and social care, rising knife crime, failing public transport, chronic homelessness and environmental challenges. Labour members including Creagh say government austerity has made neglect of poorer communities by government even more shocking.

Their intervention follows news on Friday that chaos over Brexit has forced NHS leaders to postpone a new long-term plan for the NHS and put back, yet again, a long-awaited green paper on the future of social care until January. Both decisions dismayed MPs and organisations across the health and social care sectors.

Asked why the social care green paper had been delayed, a government source told the Observer the crisis over Brexit had “wiped the grid clean and meant we have had to push stuff back. So social care won’t be until January.”

Underlining the sense of national crisis, Church of England bishops said yesterday that they would pray this weekend for national unity and “courage, integrity and clarity for our politicians” after a week of turmoil.

Nadra Ahmed, chair of the National Care Association, which represents small and medium-sized care providers, said: “If the matter wasn’t serious it could be farcical. Clearly, the government recognised in 2017 that there was an ‘urgent’ need to review the funding of long-term care to ensure we can predict a sustainable service which will meet the needs of some of the most vulnerable members of our society. We have become used to the fact that creating solutions in the growing crisis in social care is not really that urgent after all.”

Field told the Observer he had been urging May for months to allow legislation to be brought forward by select committees or through private members bills if the government could not find the time itself. But he had had no response to his idea.

Frank Field MP says he has urged the prime minister to allow legislation to be brought forward by select committees to avoid the deadlock. Photograph: David Rose/Rex/Shutterstock

Other areas of policy that MPs say have been subject to Brexit-related delays include the fair funding review, intended to reform and improve how local government financing is organised, and a government strategy on internet safety. Labour says the results of government consultations on housing issues such as longer tenancies and consumer rights – which concluded months ago – have not materialised. The domestic abuse bill, championed personally by May, also has yet to be introduced. The Missing Persons Guardianship Act, which was meant to allow the families of people who have gone missing to take control of their affairs, has not yet come into force even though it became law over a year ago.

In their statement the six select committee chairs say: “Long-drawn-out arguments over Brexit and delays in reaching an agreement on our future relationship with the EU are having a serious detrimental effect on the conduct of wider domestic policy. MPs of all parties and ministers should be addressing the most urgent challenges facing our country: safeguarding our NHS, improving social care for the elderly; stepping up the fight against crime and knife crime; sorting out our benefits system; improving our public transport and safeguarding the environment for future generations. The Prime Minister should return to addressing burning social injustices which she insisted, on entering Downing Street, would be her main priority. Instead, Brexit is sucking the life out of government at a time when our towns, cities and citizens face serious spending restraints. Rather than continuing to drag out the Brexit process for months more, we must bring it to a close if we are to prevent serious damage to our country.”

Charities, too, expressed exasperation at the government’s failure to address domestic issues, pointing to the housing crisis and chaotic rollout of universal credit. Campbell Robb, chief executive of the Joseph Rowntree Foundation, says that low-income families that backed Leave in 2016 have since been hit by price rises, spiralling housing costs and tax credit reductions. He called on the government to “get a grip and deliver for people on low incomes”. “Failing to meet their expectations of a better life after Brexit would be costly for the political parties. We need a bold package of domestic reforms, not just favourable trade terms.”

Greg Beales, who campaign director at the housing charity Shelter, said vital reforms were still needed to tackle the housing crisis and bolster renters’ rights. “But too much is currently stuck in the mire while Brexit crowds out everything else.”

Yet another policy area that has been neglected is transport, as the government has struggled to address months of timetabling chaos and pushed back the electrification of railways in the north. Darren Shirley, who heads the Campaign for Better Transport, said that there was “a bandwidth problem across government” with key domestic issues “dropping down the agenda” because of Brexit.