A study of NHS foundation trusts in England has found the number of those in financial trouble has nearly doubled in a year from 21 to 39.
Monitor, which regulates England's 147 foundation trusts, also found 18 trusts missed a target that 85% of suspected cancer patients start treatment within 62 days.
However, it said most accident and emergency departments were coping well.
A Conservative spokesman said trusts were on the whole in surplus.
Two-thirds of England's NHS hospitals are now foundation trusts. They are not directed by government so have greater freedom to decide on the way services are run.
The study by Monitor found the combined deficit of those trusts was £180m, higher than the £168m expected, with 60% concentrated in five organisations.
A further 17 trusts have "very small" deficits, Monitor said.
Mid Staffordshire NHS Foundation Trust, which runs the scandal-hit Stafford Hospital, became the first trust to be put into administration in April.
Monitor said the reasons for the breaches of the cancer target varied between the trusts, but that an increase in GP referrals "is a possible common factor".
Late referrals and consultant cover were also mentioned as other troubling issues.
Trusts did perform well against a target to see the most urgent cases within two weeks, according to the figures for October to December 2013.
The foundation trust sector as a whole has a £135m surplus so far this year, however that is lower than the planned £173m and it has "halved since this time last year, reflecting the tough financial climate and foundation trusts' response", the study said.
The Midlands is the most "financially challenged" region, with 14 of its 38 trusts in deficit, including Peterborough, Mid Staffordshire, Sherwood Forest and Milton Keynes.
Overall, 44% (33) of acute trusts, 20% (one) of ambulance trusts, 11% (two) of specialist trusts and 7% (three) of mental health trusts are in deficit.
Of the 147 trusts, 26 are currently in breach of their licence, including eight that are in special measures.
Monitor is also investigating a further eight for potential licence breaches for issues including performance failures and financial problems.
Trusts have delivered £867m of "efficiency savings" so far this year, although that is £185m below what had been planned by this stage.
Jason Dorsett, financial reporting director at Monitor, said: "All trusts need to up their game in delivering efficiency savings this year in order to maintain and improve the quality of care for patients, and ensure the sustainability of services.
"The financial trust sector is doing remarkably well in tough circumstances but is looking a little frayed at the edges."
A Conservative health spokesman said: "As Monitor themselves say, foundation trusts are performing well despite pressure on services, and are on the whole in surplus.
"This government has shone a light on poor care in a way that Labour neglected to do - and which led to tragedies like Mid Staffs - in some cases putting pressure on finances as trusts address historical issues with nursing numbers and the like.
"We are putting recovery plans in place for any trust in financial difficulty, but as the culture within our NHS changes, we do not accept that delivering safe and compassionate care in the longer term costs more money."
Shadow Health Secretary Andy Burnham said: "After a decade of improvements in cancer waiting times, progress has been derailed by David Cameron's NHS reorganisation."