Even if "hidden" costs are taken into account - the cost to the public sector of training doctors and nurses, unexpected admissions to NHS intensive care, and loss of consultants' time to the NHS - pay-bed units are still making an average profit of pounds 235 a case, the study concluded.
Multiplied up across all pay-bed activity, that is enough to keep a 25O-bed NHS acute hospital in business, according to David Cavers, managing director of Norwich Union Healthcare, which sponsored the study.
The study was carried out by National Economic Research Associates, an independent firm of consultants, who examined the accounts of six NHS hospitals whose pay beds accounted for an 11 per cent sample of dedicated pay-bed units.
Although a sample survey, it represents the most detailed examination yet of whether the NHS gains financially or not from treating private patients.
Independent hospitals - with which pay-bed units are in direct competition - have long argued that the NHS subsidises private patients. And yesterday the Independent Healthcare Association underlined that stance by calling for proper regulation of pay-bed units and transparently audited accounts of private care.
The study comes as the NHS is taking an increasing share - now up to 15 per cent - of the private-patient market at the expense of private and independent hospitals. With extra pay beds forming part of many of the new private finance deals, that share is likely to grow.
Most of the pay-bed units overestimated the "profit" they made, according to NERA's study. None the less, their average revenue was pounds 1,710 per private patient, and their average treatment cost pounds 1,400, including the return on capital which the hospitals have to make.
That pounds 310 surplus should be adjusted down to allow for junior doctors' time, the study says - an estimated cost of pounds 19. That left a financial surplus of pounds 290 per patient.
In a more pessimistic scenario, NERA says, a further pounds 56 should be knocked off to allow for lost consultant time (pounds 12), unplanned intensive care (pounds 8), training of nurses (pounds 24) and training of doctors (pounds 12). That still left a pounds 235 surplus.
Not all six units were equally profitable. Their surplus, after allowing for junior doctors' time, ranged from pounds 30 to pounds 690, but all made a surplus.
The average gain of pounds 290 per patient, "would represent around pounds 170,000 for each pounds 1m of private patient revenue," the study concludes.
Pay beds may well be more profitable than private hospitals - in part because their occupancy rates are higher at 60 per cent, against 53 per cent for private hospitals. Shared facilities with the NHS - use of operating theatres, for example - may also provide economies of scale, the study says.
The Independent Healthcare Association yesterday called for a moratorium on new pay-bed units until NHS private-patient activity was properly audited. The association also queried whether the use of government funds to allow the NHS to compete against private hospitals was legitimate.
8 Are Pay-Beds Profitable?; Norwich Union Healthcare, Chilworth House, Templars Way, Eastleigh, SO53 3RY; Free.