March 29, 2017 0312 GMT
In the most serious cases — seven of the 50 trusts that issued alerts — the hospitals declared they were unable to give patients comprehensive care, BBC wrote..
BBC Radio 4's Today program has been told operations have been cancelled and patients left waiting on trolleys.
NHS England said tried and tested plans were managing the pressures.
The Royal College of Emergency Medicine said patients in affected hospitals could face delays in receiving pain relief and antibiotics.
The Nuffield Trust health think tank released an analysis of the figures.
A new system of recording the pressure on trusts is in place this winter, known as Operational Pressures Escalation Levels.
It replaces the traditional system of hospitals declaring black or red 'alerts'.
The Nuffield Trust said NHS England figures showed 50 hospital trusts declared they were experiencing major pressures, compromising the flow of patients and had to take urgent action.
Of those, seven faced so much pressure they were unable to deliver comprehensive care and there was a higher chance of putting patients' safety at risk.
It said that although there were not directly comparable figures, as the reporting regime had changed, an analysis of two weeks in December suggested trusts declared alerts on more days than they did under the old system the previous winter.
Milton Keynes Hospital NHS Foundation Trust chief executive Joe Harrison said it had cancelled operations to free up beds.
He told Today: "We are running at somewhere around 95 percent, 96 percent bed occupancy which is very, very high."
A spokeswoman for Northampton General Hospital said it had been running at a high alert level since Monday with an unprecedented number of seriously ill patients.
Royal College of Emergency Medicine president Dr. Taj Hassan said he had met NHS England chief executive Simon Stevens and suggested emergency social care funding to help move patients out of hospital after treatment.
A spokesman for NHS England said: "NHS tried and tested plans are currently managing the ongoing pressures of this winter.
"Going into the new year, the public can play their part by avoiding going to A&E unless it is an emergency and using local pharmacy and NHS 111 for medical advice."