The warning has been made by the Royal College of Emergency Medicine in its weekly update of A&E performance.
It showed nine in 10 hospitals are increasing bed numbers - but despite this they have problems seeing patients quickly enough and discharging them.
The RCEM weekly report provides a snapshot of performance.
It covers more than 40 hospital trusts - one in five of the total.
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The update suggested that just over 86% of patients were seen and dealt with in four hours - below the 95% target.
It also highlighted problems with delayed discharges - this is when hospitals cannot release patients because services or care are not available in the community. It said in some places a fifth of beds were being taken up by these patients.
And it concluded that despite the best efforts of hospitals, winter was proving difficult and there was "insufficient capacity and capability" to respond to rising demand.
Meanwhile, official data from NHS England, which also covers last week but does not include how hospitals are performing against the four-hour target, revealed visits to A&E were increasing.
There were nearly 340,000 attendances last week, up from just under 328,000 the week before.
But Dr Barbara Hakin, of NHS England, said despite the increasing pressures staff continued to "deliver a first-class service".
"We are working hard to make sure all parts of the NHS are well prepared for the busy winter period," she added.
Scotland is also providing weekly figures for its major A&E departments. It showed that up to the start of December just over 95% of patients were being seen in four hours.
The latest data available in Wales covers October and in Northern Ireland, November. Both nations are missing the four-hour A&E target.
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Patients on two wards at University Hospital Llandough are suffering from the illness, which can pass quickly from person to person.
The hospital said the spread of the virus would be limited if people made only absolutely necessary visits.
Cardiff and Vale health board said it was asking people to be "sensible".
Chief operating officer Alice Casey said: "Many people will have the norovirus bug at this time of year - we see it every year and, for most people, it will be unpleasant but not serious.
"But when norovirus spreads in hospitals, where patients are already unwell and are in close proximity to each other on wards, the effects can be more serious."
Norovirus is a highly contagious virus which causes nausea, vomiting and diarrhoea.
The symptoms begin about 12 to 48 hours after infection and usually last for between 12 and 60 hours.

A Mount Rainier National Park spokeswoman said camping gear had been found and distress signals heard from the group's avalanche beacons.
She said there was little chance for survival.
The group, from Seattle's Alpine Ascents International, was last heard from on Wednesday.
There were two guides and four clients in the party, which began a five-day expedition last Monday.
The park spokeswoman, Fawn Bauer, told Reuters the camping gear was found more than 3,000ft (900m) below the group's last known position and the group may have been caught in an avalanche.
"We don't believe there was a viable chance for survival," she said.
The search effort has been suspended.
Ms Bauer said: "It would expose our rangers to pretty extreme conditions, so we are not able to do any kind of ground searching of that area. And, in all honesty, we may never be able to get on the ground there."
The last contact was via satellite phone on Wednesday at an elevation of 12,800ft.
At that time a rain system was sweeping through.
When the party failed to return on Friday a helicopter was despatched.
Mount Rainier stands at 14,410ft and attracts thousands of climbers each year.
A&E units across the UK are not equipped to cope with the rising demands being seen this winter, emergency care doctors say.
[NEXT_CONCEPT]
Visitors have been asked to stay away from a Vale of Glamorgan hospital because of an outbreak of norovirus.
[NEXT_CONCEPT]
Hopes are fading for six climbers who have gone missing on Mount Rainier in the north-western US state of Washington.