Health chiefs pleaded with the public on Tuesday to “avoid unnecessary illness” as the NHS faces crisis.
The viruses sweeping the country are putting added pressure on the NHS at a time when the service is already extremely stretched.
NHS Confederation Chief Executive Matthew Taylor, which represents organisations in the health service, said the situation facing hospitals was "very difficult".
"There's no doubt the situation is very difficult - that's why many trusts have declared critical incidents," he told the BBC on Tuesday.
"We are not able to provide the level of service we want to provide.
"It's important to say that the NHS is there for you if you need it, but it's also important to be clear with the public about the situation we're in and the ways in which the public can help.
"I welcome this new advice about people wearing masks and not going out if they're ill, keeping children off school, because we need to do everything we can to avoid unnecessary illness.
"The simple reality here is that the health service is caught between the fact that it has limited capacity, particularly when it comes to workforce - 130,000 vacancies - and a level of demand that it is difficult to meet in ordinary times.
"When you add in flu and Covid, which doesn't just afford a course that affects patients but also means any staff are off ill, that's when you get to this very difficult situation we're in."
Mr Taylor encouraged ministers to "consider ways of reopening negotiations with trade unions" as the NHS faces another wave of strikes this month.
Ambulance staff will walk out on January 11 and 23, while nursing staff will strike for two consecutive days on January 18 and 19. This follows industrial action by ambulance staff on December 21 and by nurses on December 15 and 20.
The Transport Secretary recommended people get vaccinated to stem the impact of Covid, and said wearing a mask is "sensible" if they need to go out while ill.
Asked if he would wear a mask if he was ill, Mark Harper told LBC: "First of all you should stay at home if you think you have got Covid or you have got flu - actually the most sensible thing to do is to not go out and spread it.
"If you do go out, clearly wearing a mask is very sensible if you are ill.
"But we manage these illnesses now by vaccination.
"People should get vaccinated for Covid, they should also get a flu vaccination. We have seen very high levels of flu this winter."
The latest NHS England data shows there were 3,746 patients a day in hospital with flu on the week ending December 25, up from 520 the previous month.
Almost 270 people in the country were in critical care beds with the virus. At the same time last year there were only 34 patients in hospital with flu, two of whom were in intensive care.
Hospitals are also grappling with increasing A&E waiting times.
The latest figures show that more than one in seven patients arriving in an ambulance at a London hospital (16.2 per cent) waited longer than 60 minutes to be handed over to staff in the week up to December 18 - a rise of over 6 per cent in a month.
Richard Webber, a spokesman for the College of Paramedics, said hospitals were unable to discharge patients because of a shortage of care workers and retirement home places.
He told BBC Radio 4:"I talked to colleagues who work in acute hospitals and they are full of patients who should be elsewhere, they should be discharged out to care homes or need support in the community.
"There is a lack of staff working in social care and a lack of capacity in social care, many hospitals have 100 or 200 patients who shouldn't be in the hospital.
"They should be elsewhere being looked after in social care, they can't be discharged, which means that the patients in the emergency department can't be admitted to hospital.
"It just seems to me completely bizarre that we have a patient who has been deemed by a consultant as medically fit to go home or to somewhere else for care is left in a bed, [but] somebody who's not medically fit sits outside on an ambulance for eight or 10 hours waiting to be admitted.
"The real problem is to get patients discharged from hospital and get the system working, and that can only be done by greater investment in social care. "
Pressures facing the NHS are "intolerable" and have become a "major crisis", the former head of the Royal College of Nursing Dr Peter Carter said.
"It is a terrible set of circumstances that we find ourselves in and we know that this is the result of years of underinvestment, particularly in social care”, he said.
"Now, because of winter, because of flu, because of Covid and all sorts of other problems, you've now got a major crisis.
"Back in August, an 87-year-old man in Cornwall spent 15 hours lying in his garden and his family put a makeshift shelter up because they couldn't get an ambulance.
"We have a crisis and there's no good people trying to dilute it.
"Right now, things are intolerable and I feel for patients, but I also feel for the staff."