Cumberland Infirmary - a PFI hospital
The profits, predicted in a report published by the GMB union, would come from the controversial private finance initiative scheme.
Under the scheme, private companies build hospitals with their own money and then rent them back to the NHS.
The report's author, John Lister, of the campaign group London Health Emergency, told BBC News Online, he was "staggered" at the sums involved.
Mortgages, which the PFI arrangements are often likened to, cost around double the original cost of the building.
Earlier this week, an independent report into Cumberland Infirmary, the first hospital to be built under PFI, said there was chaos on the wards, and urgent operations having to be cancelled.
The TUC conference in September is likely to see deep-seated opposition to PFI and other forms of private sector involvement in the NHS.
'Loan sharks'
GMB union leader John Edmonds said this latest report showed: "The government privatisation plans are effectively creating a new breed of NHS loan shark at taxpayers' expense.
"Every taxpayer is having to fork out £5 a year for the next 30 years which goes straight to these people. That is £5 which is not being spent on a single nurse or doctor."
He said the report showed that instead of bringing extra cash into the NHS, as government ministers have promised, the private sector would be "bleeding" up to £3.4 billion from the NHS in profits alone.
The report suggests the total cost of rent for PFI over the next 30 years could come to £14 billion.
Researchers say 25% of that will be profit - a sum they estimate would pay for 7,300 new nurses each year.
A spokesman for the Department of Health said all private companies which had been involved in building hospitals of providing services to the NHS since its inception in 1948, were interested in making a profit.
"Importantly, the firms involved in PFI will only make a profit if they deliver for the NHS. If they fail, they will not make a profit."