The NHS is embarking on its single biggest outsourcing of services so far by inviting bids for a contract that will be worth between £700m and £1.1bn.

The value of the deal, to provide health services including end-of-life care for older people in Cambridgeshire and Peterborough, far outstrips the previous record of £450m, where Virgin Care now provides a range of NHS services across Surrey.

The size of the contract on offer has sparked interest from a large number of private firms and claims that the privatisation of the NHS is increasing in pace. Virgin is believed to be sizing up a bid, as is another health provider, Circle, which operates the only privately run NHS hospital in the UK – Hinchingbrooke, Cambridgeshire – and Serco, which has won contracts to provide several public services and was recently castigated by MPs over major flaws in its provision of out-of-hours GP services in Cornwall.

The move is the latest example of how under the coalition growing numbers of NHS services are being put out to tender, and usually won by private operators.

Critics, including Labour, which called the new tender the "most audacious sell-off to date", say the increasing multitude of providers is leading to the fragmentation of the NHS and will undermine ministers' stated objective of ensuring that patient care is more integrated. Ministers, though, welcome the trend and support the health service's right to strike deals with providers who can offer services at the lowest price at a time when it is under huge financial pressure.

Andy Burnham, the shadow health secretary, said: "One year to the day that Danny Boyle famously celebrated before the eyes of the world an NHS that puts people before profits, we find a government stealthily breaking it up and selling it off.

"This is the most audacious sell-off to date and evidence of how, in the wake of the Health and Social Care Act, the scale and pace of NHS privatisation is ramping up."

The Department of Health denied Labour's claim that it was privatising the NHS, and hailed the "important" role non-NHS providers play.

The contract is being offered by Cambridgeshire and Peterborough clinical commissioning group (CCG), the GP-led body that organises and uses its £850m annual budget to pay for the healthcare of its 860,000-strong population. It is worth £140m to £160m a year for five years, with a possibility of a two-year extension for good performance. It will replace six separate contracts the CCG already has with NHS organisations: four hospital trusts, a mental health trust and a community services trust.

Although NHS organisations are free to submit expressions of interest by Monday's deadline, they face challenges in winning the contract as they are thought unlikely to have the range of expertise needed. The British Medical Association, which wants the NHS to remain publicly provided as well as publicly funded, voiced concern that large private firms would enjoy a major advantage over NHS rivals once the CCG starts examining the expressions of interest, which are likely to be numerous.

"The BMA remains concerned that large non-NHS providers, such as those organisations apparently interested in the older people's care contract in Cambridgeshire and Peterborough, could have an unfair advantage during the tendering process over smaller, less well-resourced competitors, especially those from the NHS," said Dr Mark Porter, chair of council at the doctors' union.

"The unacceptable damage to patient care that occurred in out-of-hours provision in Cornwall demonstrates that there are still worrying flaws in how non-NHS providers are monitored once they take over the running of NHS services. The possible fragmentation of patient care is also deeply worrying and has not been properly addressed by ministers."

Earlier this month the Commons public accounts committee criticised Serco for providing "short-staffed and substandard" out-of-hours GP services in Cornwall, falsifying data about its performance on 252 occasions and inadequate quality of service. Serco was among about 50 organisations from the NHS, private sector and third sector who attended what the CCG called a "market engagement day" to promote the contract and also bid to take over Hinchingbrooke. Serco said it could not provide a comment.

Bupa, which provides some health services but is best known as Britain's biggest medical insurer, also attended. It said it could not discuss whether it would be bidding as "it's our policy not to comment on market speculation".

Virgin Care declined to comment. If it did bid it would probably use its experience of running NHS services in Surrey, including sexual healthcare and prison medical care, to bolster its credentials.

The private healthcare analyst Vernon Baxter, the editor of Health Investor magazine, said a private firm should be able to make profits on what was the largest and longest contract of its type to date. "While providers such as Virgin Care and Serco are yet to prove definitively that they can generate a solid margin on these services, many in the private sector will believe they can take on this capitated budget, improve services and make a reasonable surplus," he said.

"Given the scale and duration of this contract, all the major players will be taking this tender very seriously indeed. There is a genuine appetite among the private sector to get into the community services market. There is a consensus that this is an area of the public sector that generates less political noise than others," he added.

Andy Vowles, the CCG's chief operating officer, said it was agnostic about whether an NHS or private provider ultimately won the contract. "What drives our GPs [on the CCG's board] is what's best for their patients, who in this case are a vulnerable group. It's not a political test as to whether it's an NHS or independent sector organisation. We are open-minded."

The Department of Health said: "There is absolutely no government policy to privatise NHS services. The NHS will stay free for everyone, but it's right that patients should get the best service – regardless of who provides it. Charities, social enterprises and independent providers play an important part in providing NHS care – and have done for many years – helping give patients more choice of where and how they are treated."

The slice of the NHS's £100bn a year budget going to non-NHS providers has risen from £5.6bn in 2006-07 to an estimated £8.7bn by 2011-12, according to a recent analysis by the Institute of Fiscal Studies and Nuffield Trust health thinktank.