A&E departments are facing extreme pressure, while the much-criticised 111 helpline has also seen a surge in patient demand, according to new data.
NHS England said 111 had seen a "huge rise in calls" last weekend - up between 24% and 30% on the same weekend last year - following a cold snap.
Just 79.9% of calls were answered within 60 seconds - against a target of 95%.
The number of emergency admissions to English hospitals has also risen compared with last week, while A&E attendances are also up.
Analysis by the BBC has found A&E departments are increasingly struggling.
It comes after several hospitals issued "black alerts" earlier this month over struggles to cope with the influx of patients to A&E.
Dr Cliff Mann, president of the Royal College of Emergency Medicine, said the NHS was reaching a "critical point" in winter.
He told the BBC: "We were beginning to think this winter would not be as bad as last winter, but the problems we are beginning to see suggest it could end up being worse.
"We have virtually no flu or norovirus - if there was to be an outbreak of either we could see the whole system tip over."
The new analysis shows some NHS trusts have had to take extreme measures to cope with the pressures.
Over the past two weeks, there have been 45 temporary closures of A&E units - up 50% on the same period last year, the BBC reported.
This means ambulances are sent to other hospitals due to the fact wards are full and waiting times are rising.
Among the problems were Coventry University Hospital cancelling all its routine operations on Wednesday and for part of Thursday because of "exceptional" circumstances.
Its chief executive, Andy Hardy, said the week had been "incredibly difficult".
The pressures built during Tuesday when more than 500 patients turned up at A&E, leading to the unprecedented step of cancelling all the routine operations, the BBC reported.
Mr Hardy said the trust had large numbers of patients in the hospital who did not need to be there but could not be discharged because there were "no spaces" in the community.
GPs in north London were also told to try to avoid referring patients to emergency departments in Ealing and Northwick Park because of "very high pressure".
A double-sized ambulance had to park outside Leicester General Infirmary last weekend as A&E staff were struggling to cope with the numbers of patients being brought in.
Bosses even discussed setting up a temporary treatment area in a tent, the BBC said.
In another example, the Royal Cornwall Hospital spent a week on black alert, which led to routine operations being cancelled. This was lifted on Thursday.
Portsmouth Hospitals NHS Trust has also spent time on black alert this week after "exceptional numbers of very sick, frail and elderly patients" needed care.
The NHS 111 non-emergency helpline - which has been deeply criticised following the death of a baby from sepsis - is also coming under increasing pressure, NHS England figures suggest.
Richard Barker, interim national director of commissioning operations for NHS England, said: "As planned for, the recent bad weather has brought a sharp increase in A&E attendances and emergency admissions.
"Despite this, A&E performance remains steady.
"The pressures remain very real, however, and we don't expect those to abate in the run-up to spring.
"This is reflected in the huge rise in calls faced by NHS 111 last weekend - up between 24% and 30% on the same weekend last year. Despite this, our frontline staff are doing a remarkable job as they continue to provide high-quality services to patients."
The latest data shows that, across England, there were 338,287 A&E attendances this week at trusts with a major A&E department, up almost 20,000 compared with 318,442 in the previous week.
There were also 94,804 emergency admissions, up on the 90,813 in the previous week.
There were 290,783 calls to 111 in the week ending January 24, a 13% increase on the 257,497 in the previous week.
The figure is up by 20% on the 241,643 calls handled in the same week the previous year.
Some 66,189 calls were received on Sunday January 24, (a 23% on the 53,822 calls received on the previous Sunday).
A spokesman for NHS England said: "The number of people using NHS 111 for their health care needs continues to grow.
"Although there is huge demand, NHS 111 continues to provide a high quality and safe service across the country, significantly reducing the burden on both A&E and 999 services."