Lockdown restrictions could be eased in March and all UK adults should have received their first dose of a Covid vaccine by September, Foreign Minister Dominic Raab said on Sunday.
"What we want to do is get out of this national lockdown as soon as possible," Mr Raab told Sky News.
"By early spring, hopefully by March, we'll be in a position to make those decisions. I think it's right to say we won't do it all in one big bang. As we phase out the national lockdown, I think we'll end up phasing through a tiered approach."
Meanwhile, NHS chief executive Simon Stevens said a Covid-19 patient was being admitted to hospital "every 30 seconds" and warned of the "extreme pressure" facing the NHS.
Speaking on The Andrew Marr Show on BBC One, he said the crisis was a "unique event" in the NHS's history, but was upbeat about the vaccine distribution and improving treatments.
People in England are being vaccinated four times faster than new cases of the virus are being detected, the NHS chief executive said, with the health service administering 140 doses a minute.
His remarks come on the eve of 10 mass vaccination centres opening across England, fuelling hopes that the target of two million doses per week can be attained, with the prospect of a return to something akin to normality by late summer.
"Our target is to have offered all the adult population a first dose by September," said Mr Raab. "If we can do it faster than that, great, but that's the road map."
Health Secretary Matt Hancock said on Sunday that over half of over-80s had been vaccinated.
The UK has been fast to implement its vaccination campaign – giving Boris Johnson's leadership a much-needed boost.
The figures may reassure the native population, but UN Secretary General Antonio Guterres is less impressed with rich nations hogging vaccine supplies. On Friday he called for more money to distribute Covid-19 vaccines to poor countries, decrying so-called "vaccinationalism".
Friday also saw the UK announce the suspension of all travel corridors from 4am (GMT) on Monday, and Mr Raab would not deny the possibility of "quarantine hotels" being established for those wishing to fly into the country.
He said that all possibilities had been considered and that enforcement of international travel restrictions would be increased.
He discouraged Britons from travelling abroad for holidays, saying it would "not be appropriate".
The government's tougher stance on travel restrictions has been fuelled by a fear that new Covid variants could evade the current vaccines and jeopardise the UK's recovery.
"We don't want to find in two or three weeks' time that our vaccine roll-out is imperilled because we haven't taken the precautionary measures on travel corridors," Mr Raab said.
The latest UK figures show the daily Covid case rate was down to 38,598, from 41,342 on Saturday. A total of 671 new deaths were reported, compared with 1,295 on Saturday, the third-highest daily Covid death toll.
Daily figures also show the number of UK vaccinations at 3,857,266, up 298,087 from Saturday's total of 3,559,179, while 4,179 patients were admitted to hospital, down slightly from 4,262 on Saturday.
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Covid around the world – in pictures
