Professor Dame Sarah Gilbert said immunity is “lasting well” for most people and suggested extra doses should be directed to countries with a low rate of vaccination.
Health Secretary Sajid Javid said he expects a booster programme to start later in September but is still awaiting advice from experts on the scale of any campaign to offer extra shots to people.
The Medicines and Healthcare products Regulatory Agency (MHRA) has said the Pfizer and AstraZeneca jabs are safe to use as boosters, but the Joint Committee on Vaccination and Immunisation (JCVI) has yet to give its advice to ministers.
Dame Sarah told The Telegraph that the elderly and people with weakened immune systems should be in line for a third jab but, “I don’t think we need to boost everybody”.
“As the virus spreads between people, it mutates and adapts and evolves, like the Delta variant,” she said.
“With these outbreaks, we want to stop that as quickly as possible.
“We will look at each situation; the immunocompromised and elderly will receive boosters.
“But I don’t think we need to boost everybody. Immunity is lasting well in the majority of people.”
On Thursday, Mr Javid said, “we are heading towards our booster programme” in England but he wanted the “final opinion of the JCVI”.
“I’m confident that our booster programme will start later this month but I’m still awaiting the final advice,” Mr Javid said.
Dame Sarah has previously highlighted the wide disparity in vaccination rates between different countries, suggesting jabs should be sent to those areas where availability is low to vaccinate everybody once, rather than some people three times.
She told the Telegraph: “We need to get vaccines to countries where few of the population have been vaccinated so far.
“We have to do better in this regard. The first dose has the most impact.”
The JCVI is expected to give its advice on who should receive a booster shot within days.
It has already said a third dose should be offered to people with severely weakened immune systems.
The expert panel is looking at the latest data from the Cov-Boost trial run by the University Hospital Southampton.
The £19.3 million UK clinical trial is testing the Pfizer jab alongside those from AstraZeneca, Moderna, Novavax, Janssen from Johnson & Johnson, Valneva and CureVac.
The study is answering key questions such as whether people who have had two doses of AstraZeneca may get more benefit if they have a third dose of Pfizer.
The new MHRA guidance says Pfizer boosters can be given to anyone, regardless of which doses they had previously.
However, AstraZeneca boosters will only be given to those who previously had the AstraZeneca jab.