People who feel unwell have been urged to wear facemasks to stop the spread of flu.
New guidance has also encouraged parents to keep their children away from school if they have a fever, and to urge them to wash their hands. Many children go back to school this week.
The number of patients in hospital with flu has risen sevenfold in a month, according to the latest data.
Health chiefs said the NHS was suffering a “twindemic” as hospital admissions for flu have increased and cases of Covid have risen.
Professor Susan Hopkins, the chief medical adviser at the UK Health Security Agency (UKHSA), said: “If your child is unwell and has a fever, they should stay home from school or nursery until they feel better and the fever has resolved.
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“Adults should also try to stay home when unwell, and if you do have to go out wear a face covering.”
On Christmas Day there were 3,849 patients in hospital with flu, 100 times more than last year, NHS England figures showed. Last month hospital admissions for flu increased, from 520 a day in November. The number of patients in hospital with the coronavirus has doubled in a month, to 9,459.
In the week of Christmas, 8,000 NHS staff were also off sick with Covid.
The UKHSA added that “high numbers of scarlet fever, which is caused by group A streptococcus, also continue to be reported”.
Pupil absence rates in schools across England rose sharply at the start of last month because of illness. The proportion of children off sick rose to 7.5 per cent in the week beginning December 5 from 6.1 per cent the previous week.
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James Bowen, director of policy for the school leaders’ union NAHT, said: “There does appear to be an unusually high level of illness around at the moment, even for this time of year.
“Advice from government is welcome to give schools and parents clarity on when children should stay at home.
“It is quite common for school policies to already state that children with a fever should remain at home, so this shouldn’t represent a major departure from existing policies.”