The figures for April to June showed NHS Foundation Trusts had a deficit of £445 million.
Other NHS trusts ended the first quarter of the year £485 million in deficit.
The foundation trust sector is “under massive pressure” and can no longer afford to go on as it is, the financial regulator Monitor said.
The new report from Monitor covers 151 NHS foundation trusts, while a separate study from the Trust Development Authority (TDA) covers 90 NHS trusts.
Of 90 trusts in the TDA report, 72 ended the financial quarter in deficit.
Some 118 foundation trusts (78%) covered by Monitor also ended the period in debt. The overall deficit of £445 million was £90 million worse than planned.
Some 75% of those in deficit were acute hospital or specialist trusts.
The main cause of overspend among foundation trusts was higher than expected costs for staff pay, with an “over-reliance” on expensive agency staff, Monitor said.
Foundation trusts also missed a number of national waiting times targets, including the A&E target for people to be seen within four hours. Targets for routine operations and some cancer treatments were also missed.
A lack of beds meant 29,000 people waited on a trolley for more than four hours between the decision to admit them to A&E and their arrival on a ward.
Across England, the waiting list for routine operations reached 1.9 million people - a 169,100 increase on the same period in 2014/15.
Some 10,800 patients also waited longer than the recommended six weeks for diagnostics tests.
However, trusts did meet a target of treating non-emergency patients within 18 weeks.
Monitor said trusts had further “struggled to deal with an increase in demand for diagnostic tests, partly due to staff shortages and ineffectively organised services”.
It warned that trusts must make “radical and lasting” changes to how care is delivered.
Dr David Bennett, chief executive at Monitor, said: “Trusts are working hard to provide patients with quality care.
“However, today’s figures reiterate that the sector is under massive pressure and must change to counter it.
“The NHS simply can no longer afford operationally and financially to operate in the way it has been and must act now to deliver the substantial efficiency gains required to ensure patients get the services they need.”
Foundation trusts made £232 million worth of cost savings - which was £64 million less than planned.
Monitor intervened or agreed regulatory action at 37 trusts (25% of the sector) because of operational or financial concerns.
Last year, NHS trusts and foundation trusts overspent by £820 million.
It has been suggested that the deficit among the trusts could top £2 billion for the whole of the financial year.
Health Secretary Jeremy Hunt has announced a cap on the use of expensive agency staff, which currently cost the NHS more than £3 billion.
The NHS has been paying agencies up to £3,500 per shift for doctors, and the total bill for management consultants was more than £600 million last year.
Unite union national officer Barrie Brown said: “The financial chickens are coming home to roost big time.
“This is what happens when you have growing demand for NHS services and then decide to impose £20 billion of so-called ‘efficiency savings’.
“Health Secretary Jeremy Hunt needs to start banging the Cabinet table to get more funds in real terms from the Chancellor, George Osborne, otherwise the NHS will go into a financial meltdown.”
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