Yes, they are offered for free. If you are elderly, pregnant, immunosuppressed, live/care for vulnerable people, or have a variety of other health conditions including asthma, you get offered a free flu jab every autumn on the NHS .
https://www.nhs.uk/conditions/vaccinations/flu-influenza-vaccine/
The current criteria for qualifying for an NHS winter COVID vaccine are far stricter than the criteria for the NHS flu vaccine.
If you are asthmatic, you can easily be considered vulnerable enough to need the flu vaccine, but still not qualify for the COVID vaccine.