The Green party MP Caroline Lucas has called on Labour to support a bill that would reverse much of the Conservatives’ NHS reforms, and was previously backed by Jeremy Corbyn.

The private member’s bill, named the NHS reinstatement bill, received cross-party support when it was first introduced to parliament in July, and was signed by Corbyn, the Labour leader, and the shadow chancellor, John McDonnell, when the pair were backbenchers.

The bill would reinstate the secretary of state’s responsibility for the health of UK citizens, something the Health and Social Care Act removed. It would also abolish bodies such as NHS trusts, NHS foundation trusts and clinical commissioning groups, allowing commercial companies to provide services only if they were essential to patient welfare and the NHS could not do so itself.

A private member’s bill can be introduced by any member of parliament or peer who is not a government minister, but few of them actually pass in to law because they are given little parliamentary time. Lucas’s bill will be given its second reading on 11 March.

It is Labour policy to repeal the Health and Social Care Act and a party spokesperson said: “Labour is reviewing the latest draft of the bill and consulting with experts and patients on the details.”

“Across the UK people are fighting tooth and nail to protect our NHS,” said Lucas. “From junior doctors defending their right to a fair and safe contract, to local communities like my own standing up to the threatened closure of GP surgeries – the government’s mistreatment of our health service is being matched by righteous indignation.”

Lucas said the bill sought to reverse the creeping marketisation of the health service and to reinstate the NHS based on its founding principles. “It’s now time for politicians to unite in forwarding an alternative to inefficiencies of the marketisation programme currently gripping our NHS,” said Lucas.

“The NHS bill would put the public back at the heart of the health service. Labour should now put their commitment to a public NHS into action by backing this bill. Unless we work together the chances of saving our crisis-ridden health service diminish by the day.”

Lucas first introduced an almost identical version of the bill – which she worked on with the former Liberal Democrat MP Andrew George – to parliament in March 2015, but parliament broke up for the summer recess before it had a chance to progress into law.

In June 2015, a conference of the British Medical Association backed Lucas’s proposed NHS reinstatement bill by 53% of the vote, but doctors and medical students stopped short of calling for the BMA to lobby the government for it to be adopted.