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
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A waiter carries dishes from outdoor seating as indoor dining reopens in a limited capacity to reduce the spread of coronavirus in Philadelphia, Pennsylvania, US. Reuters -
Hamilton at Richard Rodgers Theatre near Times Square remains closed following restrictions imposed to slow the spread of coronavirus in New York City. The pandemic has caused long-term repercussions throughout the tourism and entertainment industries, including temporary and permanent closures of historic and iconic venues, costing the city and businesses billions in revenue. AFP -
People drive through the Jurassic Quest Experience outside The Rose Bowl Stadium in Pasadena, California, US. Reuters -
Joyce Flippin, 83, receives a dose of the coronavirus vaccine at Mission Commons assisted-living community in Redlands, California, US. Reuters -
Hudson Mahaffay reacts to a staff member dressed like a raptor at the Jurassic Quest drive-thru Experience outside The Rose Bowl Stadium in Pasadena, California. Reuters -
People drive through the Jurassic Quest Experience outside The Rose Bowl Stadium in Pasadena, California. Reuters -
A nurse checks in on a person in a vehicle after receiving a dose of a coronavirus vaccine at a drive-through vaccination site at the TCF center in Detroit, Michigan, US. Reuters -
The empty streets of Montmartre as the 6pm curfew starts in Paris. The prime minister announced last Thursday an extension of the 6 pm-to-6am curfew to cover the whole country, including zones, like Paris, where it previously hadn't started until 8pm. AP Photo -
A couple walk on the Trocadero square near the Eiffel Tower during the curfew in Paris. All of France is under a stricter curfew, which started on Saturday at 6pm and will last for at least 15 days. AP Photo -
A general view outside the stadium prior to the Premier League match between Leicester City and Southampton at The King Power Stadium in Leicester, England. Sporting stadiums around England remain under strict restrictions as social-distancing laws prohibit fans inside venues, resulting in games being played behind closed doors. Getty Images -
A photographer sits between cardboard cu- out fans during the Sky Bet League One match between AFC Wimbledon and Sunderland at Plough Lane in Wimbledon, England. Getty Images -
A man wears a face mask as he rides a motorcycle in Karachi, Pakistan. Many countries around the world are battling a surge in coronavirus infections. EPA -
People wearing protective masks stand in front of a poster featuring a photograph of India's Prime Minister Narendra Modi outside the All India Institute of Medical Sciences in New Delhi, India. India launched one of the world’s largest coronavirus vaccination drives on Saturday, setting in motion a complex deployment plan aimed at stemming the wide spread of infections across a nation of more than 1.3 billion people. Bloomberg -
A robot serves customers at a Japanese robot restaurant in Bangkok, Thailand. Thailand's first Japanese robot restaurant, Hajime, where the serving waiters are robots, has been operating since 2010, serving Japanese food shabu, yakiniku and sushi. EPA -
A man walks past restaurants which closed after 8pm, the time the government asks them to close by, amid the coronavirus emergency decree in Tokyo, Japan. Reuters -
People pray outside Hasan Anani mosque in Jiddah, Saudi Arabia. AP Photo -
A street is almost empty of cars during an 11-day nationwide shutdown aimed at curbing the spread of the coronavirus, in Beirut, Lebanon. Lebanon's parliament has approved a draft law to allow the importing of vaccines into the tiny country to fight the spread of coronavirus. AP Photo
