Hospitals are under such pressure that patients are being forced to sleep in corridors because there are too few beds for them on wards, the leader of Britain's nurses has revealed.

Dr Peter Carter, the chief executive of the Royal College of Nursing (RCN), said the practice showed that the NHS was under unprecedented strain.

"In all my time in this job, I've never received more emails, calls and letters about the strain on the NHS and colossal workload you face. Nurses have given me accounts of patients being forced to sleep in corridors," Carter told the RCN's annual conference in Liverpool.

Patients and their families react badly when it happens, said Carter, who is also the 415,000-strong union's general secretary. "Patients and their relatives are often so exasperated that they have been taking pictures of nurses on their smartphones and demanding to know the names of nurses," he added, citing the practice as evidence of nurses facing "unrelenting pressures" and being put in "an unacceptable situation".

In his speech to several thousand RCN delegates, Carter renewed his attack on what he said were dangerously substandard staffing levels in too many hospitals, which were putting patients at risk.

"The government can't keep kidding itself. It can't keep labouring under the illusions that numbers don't matter – the facts prove they do."

He cited the recent disclosure by the Care Quality Commission, the NHS watchdog in England, that 16% of hospitals it regulates have what it considers to be inadequate numbers of staff.

The RCN wants the NHS to introduce legally enforceable minimum levels of staffing, and Carter criticised the health minister Dan Poulter's view that such a requirement would lead to a "race to the bottom" on staffing in the NHS.

"How much longer do we have to wait with wards without enough staff? How many more patients need to suffer unnecessarily?" Carter asked.

Carter also criticised the health secretary, Jeremy Hunt, over other government plans in its recent response to the recommendations made by Robert Francis QC in his report in February into the Mid Staffordshire hospital trust care scandal.

Hunt's plan for would-be nurses to spend a year before they start studying for their nursing degree working as healthcare assistants (HCA) "feels like it was written down on the back of a napkin" and has "more holes in it than Swiss cheese", he said.

The RCN had failed to find out so far where the money to pay for it would come from, who would pay the 210,000 aspirant nurses as they worked as HCAs and who would decide which of them were allowed to start training. The policy, which received widespread coverage, would eventually be dropped, Carter predicted.

He also took Hunt to task for refusing to endorse Francis's recommendation that healthcare assistants should be regulated and said hospitals needed to employ more ward clerks and administrative assistants to lessen the load on nurses of having to fill in forms continually so they could spend more time caring for patients.

But Hunt accused the RCN of allowing its trade union role to trump its duty as a royal college to raise standards within the profession.

His comments came after the RCN president, Andrea Spyropoulos, condemned plans to require new recruits to work for 12 months as a healthcare assistant before beginning their nursing training as a "really stupid idea".

But Hunt insisted that many nurses supported the plan, while pointing out that the RCN had come in for criticism in the Francis report on the Mid Staffs scandal.

"I think the Royal College of Nurses [sic] has to be very, very careful. They missed what happened at Mid Staffs," he told Sky News.