“I strongly encourage as many people as possible to get vaccinated this season.
“Don’t wait until we reach the winter peak, get your vaccinations early.”
Those eligible for free Covid-19 boosters this year include adults aged 75 years and older, residents in care homes for older adults and individuals who are immunosuppressed, aged six months and over.
People aged 65 and older are eligible for free flu jabs, along with those in care homes, close contacts of immunocompromised individuals and pregnant women.
All children aged two or three on 31 August, all primary and secondary school children and those aged 18 years to under 65 in clinical risk groups are also eligible for the free flu vaccination.
The trust said those eligible would be invited to get their boosters but other people would have to wait to book.
Chief nursing officer Carolyn Mills said flu viruses change from one winter to the next and they were updated each season to give the “best possible protection”.
