The public are being reminded to come forward for their flu jab to maximise their protection ahead of winter.
Health officials are worried because this will be the first winter Covid and flu circulate fully at the same time.
Research shows those infected with both viruses are more than twice as likely to die as someone with Covid alone.
More than 40 million people across the UK - 35 million in England - are being offered a jab this year in the biggest flu vaccination campaign so far.
And this includes, for the first time, all secondary-school children up to the age of 16.
Alongside the extended flu campaign, the over-50s and younger adults with health conditions are also being offered a Covid booster jab this autumn and winter.
Dr Jenny Harries, head of the newly formed UK Health Security Agency, warned the level of immunity to flu was likely to be lower this winter because very little of the virus had been circulating last year, because of social distancing and lockdown.
"It is really important people get vaccinated," she said.
"This is the first winter where we will have seasonal flu and Covid co-circulating."
Prof Wendy Barclay, professor of virology at Imperial College London, told the BBC's Today Programme that it had been trickier to gauge which flu strains to cover with this year's vaccine because cases had been so low last year.
"The vaccine this year is updated to match what we predict will be the circulating strains," she said.
England's deputy chief medical officer Prof Jonathan Van-Tam said "we need to take this seriously and defend ourselves" by taking the vaccines when offered.
"Both these viruses are serious: they can both spread easily, cause hospitalisation and they can both be fatal," he said.
Flu kills about 11,000 people on average every winter in England and during the last bad flu winter of 2017-18 the toll was more than double that - with more than 300 deaths a day during the peak.
Flu and the other winter viruses also lead to more than 1,000 hospital admissions a day in winter months - more, currently, than is being seen for Covid.
And this winter, respiratory illness could hit very high levels, causing severe strain on the NHS and up to 60,000 deaths, according to a report from the Academy of Medical Sciences.
Respiratory syncytial virus (RSV), the leading cause of hospital admission in the under-fives, is already circulating at much higher levels than normal.
The winter warning comes as the government launches an advertising campaign, featuring TV medics Dr Amir Khan, Dr Dawn Harper and Dr Karan Ranj, to encourage those eligible to come forward for both the flu and Covid boosters.
The following groups are among those eligible for winter vaccines:
- over-50s (Covid booster and flu jab)
- younger people with health conditions (Covid booster and flu jab)
- health and care workers (Covid booster and flu jab)
- pregnant women (flu jab)
- two- to 16-year-olds (nasal flu jab)
- at risk infants aged six months to two years (flu jab)
GP surgeries will contact patients eligible for the free NHS flu vaccine or eligible patients can book an appointment at a pharmacy.
People who qualify for the coronavirus booster are being told to wait until they are contacted.
Anyone who is not eligible for a free flu jab can pay for it privately at many pharmacies, at a cost of about £15.
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What questions do you have about the flu vaccine?