The government has abandoned plans to privatise an NHS employment agency it owns that supplies doctors and nurses to hospitals to ease their understaffing.

Labour welcomed what it called “a major U-turn on a misguided policy from a government with no solution to the workforce crisis in the NHS”.

Ministers decided last year to sell off a 75% stake in NHS Professionals, which is fully owned by the Department of Health. The move sparked widespread concern and criticism from MPs, doctors and health unions, who argued that the sale was foolish given the seriousness of the NHS’s worsening staffing crisis.

NHS Professionals, which was set up by the last Labour government, plays a key role in the NHS. It supplies doctors, nurses and other staff to about a quarter of hospitals at much cheaper rates than those charged by profit-making NHS staffing firms and saves the cash-strapped NHS £70m a year that would otherwise go to private firms.

Philip Dunne, the health minister, announced the U-turn in a written ministerial statement issued this morning at the unusually early time of 8am.

He blamed the change of policy on bidders not offering enough money for the 75% stake and did not acknowledge the wave of opposition the planned sell-off had generated. Ninety-five opposition MPs – from Labour, Lib Dems, SNP and Plaid Cmyru – and one DUP MP had signed a Commons early-day motion backing an immediate halt to the sell-off.

Dunne said: “NHS Professionals Ltd – a company which supplies flexible staffing to the NHS – will remain in wholly public ownership, after offers to buy a majority stake in the company undervalued its growing potential.”

He outlined how the firm “currently holds a bank of over 90,000 workers filling more than 2m shifts, saving the NHS £70m every year”. Since the DH decided to sell NHS Professionals its performance had risen, with the result that its pre-tax profit – which goes back into the NHS – rose 44% last year compared to 2015-16, he said in the statement.

“Ministers tried to push through a sale behind closed doors but have been forced to abandon their plans in the face of wide opposition from NHS staff and patients,” said Justin Madders, the shadow health minister, who had asked the National Audit Office to investigate the sale.

“With huge workforce shortages across the health service, NHS Professionals plays a crucial role in organising last-minute or replacement staffing. This is an effective and successful public body which saves the taxpayer around £70m a year,” added Madders. Ministers should disclose how much money had been spent so far on the now ditched sale, he said.

With its future in public hands now guaranteed, NHS Professionals needs to expand the number of NHS trusts it works with in order to reduce their reliance on “more expensive agencies”, Dunne said.

Cat Hobbs, director of the campaign group We Own It, which helped organise opposition to the sale, said: “This is a huge victory for the NHS and everyone in this country. The public doesn’t want to see senseless privatisations and they have stood up and said no to this one.”