Thinktank says many hospitals could become unsustainable and current system is not equipped to deal with the problem

One in three hospitals could end up in major financial difficulties in the next few months as a result of an unprecedented NHS-wide cash squeeze, experts have warned a parliamentary inquiry.

In a bleak assessment of the service's financial future, the Nuffield Trust health thinktank has told MPs so many hospitals could become unsustainable and that the current system of bailing out those which go into the red is not equipped to deal with the scale of the problem. Ministers should prepare for that scenario because it is highly likely to unfold, says its submission to the Commons health select committee's inquiry into the NHS's ongoing £20bn savings drive.

The trust has told MPs that its analysis of official data about the NHS's financial health shows "many hospitals face severe and potentially unsustainable financial pressures", and thus have a question mark over future viability.

Smaller hospitals and those which have not attained foundation trust status, and are thus semi-autonomous of NHS and Whitehall control, are most at risk. Hospitals in "regional clusters of financial stress", such as outer London and the West Midlands, are also in the same difficult position, the trust adds.

Of the 246 different types of NHS trusts providing care in England 83 are not earning enough, or generating a sufficient surplus from their work, for Monitor, the service's economic regulator, to grant them foundation trust status, the Nuffield Trust says. They include 40 of the 146 foundation trusts and 43 of the 100 trusts which have not achieved that status.

The NHS's habit of bailing out hospitals in trouble can no longer be maintained because "hospital trusts could start becoming unsustainable in larger number than the current system is designed to address", according to the trust.

Trusts have been hit by tariff payments – the amount they receive for providing a certain course of treatment – falling by 12% in real terms since 2010-11 as part of the NHS's "Nicholson Challenge" to make £20bn of efficiency savings by 2015.

Labour seized on the thinktank's analysis. "Ministers lack a plan to deal with trusts in serious financial difficulties and cannot guarantee that the quality of patient care will not be affected. With hospital trusts facing a financial challenge, the government should be focusing on sorting the situation out," said Andy Burnham, shadow health secretary.

Anita Charlesworth, the trust's chief economist, said: "We need to monitor the signs that this challenging situation could lead to an unsustainable financial squeeze on hospital trusts. The weakest hospitals appear to be getting weaker."

But the Department of Health insisted: "The NHS is in good financial health and is performing well for patients. We know it faces increasing pressures but it is on track to make £20bn of efficiency savings by 2015."

It has already saved £10.8bn of the £20bn in the years 2010-11 and 2011-12, a spokeswoman said.