An expert has expressed concern that the first priority groups will not all receive their Covid-19 booster jabs by Christmas.
John Roberts from the Institute and Faculty of Actuaries said he worries that at the current rate the first priority groups one to nine may not get vaccinated until mid-January.
But the NHS in England disputed the figures Mr Roberts used, saying that six weeks into the initial rollout it had delivered 4.1 million jabs, and six weeks into the booster programme it had delivered more than seven million boosters.
Mr Roberts told BBC Radio 4's Today programme: "We have now vaccinated around about two-thirds of the over 80s and three quarters of those who are eligible, and I think we're going to start to see over the next few days that that will start to come through, first in cases and then in hospitalisations and deaths.
"And so we are going to see that benefit coming through but we could have done it a lot quicker than we're doing it at the moment.
"And my worry is that, at the current rate, we're still not going to complete the first priority groups one to nine until mid-January.
"And that's going to mean that there's going to be a lot of mixing over Christmas with festive behaviour before and then on the day of people who haven't got that extra protection from the booster, which really does make a huge difference.
"The analysis that we're getting from Israel is that it will probably reduce deaths by 80 or 90% even.
"So it's important that we get on with it as quickly as possible."
His comments come as figures show the NHS delivered a record number of boosters last week.
Around 1.7 million coronavirus booster jabs were given out - the highest weekly total yet, the NHS in England said.
So far more than eight million booster jabs have been delivered across the UK - including 820,000 since Friday.
The NHS in England disputed the figures Mr Roberts used, saying that six weeks into the initial rollout it had delivered 4.1 million jabs, and six weeks into the booster programme it had delivered more than seven million boosters.
And the NHS has ramped up its efforts to get people to have the jab when offered and opened up hundreds of walk-in sites across the country for those eligible.
Experts have warned that waning immunity from the vaccines could lead to a rise in severe disease and hospital admissions.
Most will be offered the top-up jab six months after they received their second dose, with a few at highest risk offered it sooner.
