Lockdown restrictions could last for longer than the current mid-February prediction, with the Health Secretary saying that measures will be in place for "as long as they are necessary."
Matt Hancock said the vaccination programme was "on track" to deliver the jab to the 14 million most vulnerable people by February 15.
But he told Sky News that it was "impossible to know" when restrictions could be eased.
He said: "We will keep the restrictions in place not a moment longer than they are necessary, but we will keep them in place as long as they are necessary.
" These measures that we have got in place that we hope to be able to lift, and we should be able to lift when we have been able to protect through vaccination those who are vulnerable - right now the vaccination is not in a position to do that."
Professor Anthony Harnden, deputy chairman of the Joint Committee on Vaccination and Immunisation (JCVI), told Sky News that measures such as social distancing will be needed "for a while yet", even among those who have received the jab.
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He said: "We must be very clear that vaccination will prevent disease in individuals but it may not prevent those individuals from transmission to others.
"So, even though you've been vaccinated, you might not be completely protected yourself, you may be at risk of transmitting to others, so I think we will have to use extra precautions in terms of social distancing, wearing masks, for a while yet."
But he said there was hope for the future and predicted that by March cases and hospitalisations would be much lower.
He added: "There is light at the end of the tunnel and certainly by the beginning of March we should see a sharp drop off in hospitalisations and deaths."
