But that fell far short of the £4 billion in additional funding that Simon Stevens, the chief executive of the service in England, requested last year, warning that services would come under unprecedented pressure during the winter.
“The N.H.S. waiting list will grow to five million people by 2021,” Mr. Stevens said in an impassioned speech to health care leaders in November. “That is one million more people, equivalent to one in 10 of us, the highest number ever.”
What’s more, he said, “after seven years of understandable but unprecedented constraint on the current budget, the N.H.S. can no longer do everything that is being asked of it.”
Over the past week, hospitals have increasingly declared “black alerts,” an admission that they are unable to cope with demand, the health service confirmed, without releasing numbers. Most hospitals have been unable to meet emergency-ward targets of seeing patients within four hours because of a shortage of beds and staff.
Prime Minister Theresa May denied that the National Health Service was facing a crisis. “The N.H.S. has been better prepared for this winter than ever before, we have put extra funding in,” she said on Wednesday. “There are more beds available across the system. We’ve reduced the number of delayed discharges of elderly people who would otherwise have been in N.H.S. beds rather than in social care,” she added, referring to state-funded care.
But the scenes unfolding across hospitals in Britain paint a different picture.
Tuesday night, the emergency ward at Kingston Hospital in southwestern London looked more like an airport lounge than a hospital, with patients sprawled out in the waiting room.
“There’s no real system or order; it’s a jungle in here,” said Nancy Harper, who had accompanied her 87-year-old grandmother, who was lying down and complaining of excruciating pain in her lower back.
“It’s been more than five hours,” Ms. Harper said. “We get to the front of the queue and then someone more ill comes in and we get pushed back. It’s outrageous.”
Other patients said they had been turned away and referred to a pharmacy or general practitioner because their cases were not deemed urgent enough.
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“I don’t even think I was seen by a nurse,” said Ali Elamine, who complained of acute ear pain. “Some helper just took my temperature, said it was normal and told me to go to my local G.P. in the morning.”
Many hospitals have asked that patients seek help from emergency rooms only for urgent or life-threatening matters.
More than nine million people at emergency wards in the 2016-17 fiscal year were sent home after receiving only guidance that in many cases could have been obtained from a pharmacist, the health service said in a statement on Tuesday.
And Jane Cummings, the chief nursing officer for N.H.S. England, said that millions of patients had missed hospital appointments last year, at a cost of almost £1 billion.
“With the N.H.S. coming under pressure as never before, we are asking patients and the public to use the health service responsibly,” she said, “to help ensure that care is readily available for everyone who needs it.”
Dr. Anu Mitra, an emergency physician at Imperial College Healthcare N.H.S. Trust, said that 70 years ago, as the country was recovering from the devastation of war, the health service had been the country’s “greatest gift.” But “awful days like today” are a result of a systematic dismantling of the system eight years in the making.
“Two years ago I’d have point blank refused to examine a corridor patient until they were in a cubicle,” Dr. Mitra said on Twitter early Wednesday. “On days like this it’s unavoidable, I’m ashamed to say.”
The extraordinarily high pressure has led to resignations. In December, Bob Kerslake, the chairman of the board at King’s College hospital in London, quit in protest over what he viewed as the government’s insufficient funding of health services.
“We desperately need a fundamental rethink,” he wrote in an opinion piece in The Guardian.
Health Secretary Jeremy Hunt apologized to patients on Wednesday for the postponement of thousands of nonurgent operations. “It is absolutely not what I want,” he told Sky News. “There are real pressures, no doubt about it. This is the busiest week of the year for the N.H.S.”
Patients have accused hospitals of putting them at risk.
“I learned about the new set of deferrals from the news, but if I receive a notification, it will be the third time my operation is postponed,” Graham Groves, a construction worker, said as he sat in a cafe at St. Mary’s Hospital on Wednesday. “This is a disgrace. We injure ourselves while working to pay our taxes, and the government just leaves us to suffer.”