People aged 65 or over can book a slot for getting a booster vaccine on the NHS website, or by calling 119.
The vaccines will soon be provided for free to more vulnerable groups, the NHS said.
“Hundreds of thousands of adults who are eligible for winter vaccines – including all aged 65 and over, pregnant women and those with an underlying health condition – will also begin receiving invitations from the NHS to encourage them to get their Covid and flu jabs from this week,” a statement said.
The rollout of boosters has been brought forward as the new Covid variant Pirola has led to spike in cases. Pirola is a new mutation of the Omicron strain of Covid-19 which has worried experts with increasing cases.
There have been 37 cases recorded so far in England, while Scotland has recorded five cases. Testing for Covid-19 has reduced in recent weeks, making it difficult to keep track of the actual rate of infections.
“The new Covid variant presents a new risk, but NHS staff are rising to the challenge once more to do all they can to protect the public,” NHS director for vaccinations and screening Steve Russell said.
“Vaccines are our best protection against flu and Covid-19, and I strongly encourage all eligible people to come forward for their lifesaving winter vaccines as soon as they can.”
Data released earlier by the UK Health Security Agency (UKHSA) showed hospital admissions for patients who tested positive for Covid-19 stood at 4.6 per 100,000 people in the week to 10 September, up from 3.7 per 100,000 the previous week. This is the highest since the week ending 30 April.
This is still some way below the level reached at Christmas 2022, when the rate stood at 11.8 per 100,000, and is also well below the figures seen during the first year of the pandemic.
Intensive care admissions also remain low, but overal Covid hospitalisation numbers have been on a clear upward trend for the past two months.
Vulnerable groups, especially people above the age of 85, make up most of the hospitalisations seen in recent weeks.
“We are already seeing a slow rise in cases of Covid-19, as well as increases in hospitalisations, particularly among the over 75s,” said Dr Mary Ramsay, head of immunisation at the UKHSA.
“Older people and those in clinical risk groups remain at higher risk of severe illness, so it’s important all those eligible come forward when offered and get protected against flu and Covid.”