LONDON — A day after denying that the National Health Service was facing a crisis, Prime Minister Theresa May of Britain apologized on Thursday for delays throughout the health care agency as it scrambled to cope with a particularly difficult winter season.

“I know it’s difficult, I know it’s frustrating, I know it’s disappointing for people, and I apologize,” she said in a television interview after being asked if she would be happy if a relative were put through the delays that patients were facing.

A flu outbreak, colder weather and high levels of respiratory illness have put an unusually severe strain on the N.H.S. this winter, forcing the service to postpone thousands of nonurgent surgeries and outpatient appointments to free up hospital beds and staff.

And all that comes against a backdrop of years of austerity-driven budget restraints, as well as staffing shortages that many health experts attribute to the anti-immigrant atmosphere fostered by Britain’s withdrawal from the European Union, which is driving foreign health care workers back to their home countries.