Private firms now treat almost one in five NHS patients with certain conditions due to the last Labour government's embrace of competition, an authoritative study reveals.

Allowing profit-driven health firms to be paid out of NHS funds has seen private operators grow from doing very few state-funded procedures to now being a "significant" provider of care, the Institute for Fiscal Studies (IFS) said in a report commissioned and funded by the Nuffield Trust

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Private firms have made such inroads that independent sector treatment centres – facilities set up to treat NHS patients – now carry out 17% of hip replacements (11,500 operations), 17% of hernia repairs (9,000) and 6% of gall bladder removals (3,000) annually in England. Their share of NHS patients grew rapidly between 2006-07 and 2010-11 after Labour's promotion of patient choice.

By 2010-11 private providers also handled 8% of patients' first attendances in relation to orthopaedics or trauma, such as a broken limb; 4.8% of such attendances for gastroenterological problems; and 2.3% of attendances for sight problems.

In 2006, GPs typically referred patients to an average of 12 different healthcare providers a year, mainly in the NHS. By 2010 that had risen to 18, mainly because they were encouraged to offer patients a wider list of places to be treated.

The disclosure of how dramatically private firms expanded their role in the NHS during Labour's time in power may prove politically difficult for the party, which regularly attacks the coalition for seeking to increase competition.

Labour said using independent centres had been necessary to clear a backlog of patients waiting for treatment and was unlike the coalition's greater use of the private sector, which it accused of weakening the NHS by opening its "core" to competition. "Under Labour these agreements supplemented the mainstream NHS – giving it the extra capacity it needed to deliver the lowest ever waiting lists. This is very different to the current government's privatisation of the core of the NHS," said Jamie Reed, a shadow health minister and MP for Copeland.

"'Any qualified provider' [which lets private firms bid to run community health services] puts the private sector on the same footing as the NHS when competing for contracts. If the NHS loses out then its capacity to provide that service will shrink. The NHS must always be given the first opportunity to provide its own services," Reed added.

A party spokesman added: "The last Labour government used these agreements to add extra capacity to the NHS and allow patients to be treated in record times. This Government's eagerness to hand contracts to the private sector, in place of the NHS, whittles away the health service's own capacity – that's why the next Labour government will repeal this dangerous free-market free-for-all".

The NHS Partners Network, an alliance of private providers of NHS care which is part of the NHS Confederation, said the findings showed GPs have been directing patients to non-NHS treatment services because they are better."This is further evidence that patients do indeed want to have choice and will take advantage of it where it is in their interests to do so.

"It is also significant that the exercise of choice is now increasingly being supported by GPs where they consider it to be right for their patients. That means most GPs are, as one would expect, putting patients before politics," said David Worskett, its director.

There are now 195 independent hospitals and treatment centres in England where patients can be treated at NHS prices under the "choose and book" system, which has significantly expanded choice, Worskett added. "While the overall proportion of NHS care delivered by the independent sector remains very low, at less than 5%, independent providers are very pleased to be making what is clearly a valued contribution to the NHS and patients in these challenging times.

"Quite obviously, as this study shows, the vast majority of patients continue to use their nearest NHS hospital, but where an alternative is more convenient or appropriate, patients clearly welcome this," he said.

The latest official data from the NHS's Health and Social Care Information Centre shows that the trend of growing numbers of NHS-funded procedures being carried out by private firms has continued under the coalition. They gave 345,200 NHS patients non-urgent treatments such as knee replacements and cataract removals in 2011-12, up almost 33,000 in a year, though that represented just 4.3% of all the 8m such procedures carried out that year, up from 4% a year earlier.

The British Medical Association said increasing competition could ultimately threaten the viability of NHS services. "The BMA has had concerns for a number of years about the ethos of promoting competition between different providers within the NHS as this could lead to a fragmentation and possible destabilisation of patient services," said a spokesman.

Lord Howe, the health minister, said the quality of patient care and the fact it was free, not who provided it, was what mattered most. "The crucial thing here is that patients have access to the best possible services on the NHS and that they do so according to the founding principles of the health service – free at the point of delivery and available to all on the basis of need," Howe said.

He defended the coalition's expansion of private provision in the NHS, which has raised concern about wholesale privatisation. "We want to give patients more choice about where, when and how they can access their health services and patients are clearly making choices about services that meet a broad range of their needs."

• This article was amended on 20 November 2012 because the original omitted the information that the IFS report was commissioned and funded by the Nuffield Trust.