Experts have said social distancing measures may be needed all year, and a cabinet minister has said it's too early to predict what the situation will be come autumn.
Liz Truss, the international trade secretary, told Sky News it is "not wise" to make long-term predictions, after modelling by a sub-group of SAGE showed that even with a vaccine that can stop transmission, lockdown would need to last until May and social distancing until the end of the year.
Ms Truss said the government would be taking decisions on a "week-by-week basis" as it continues to monitor the path of the disease.
Recent modelling by the group at the University of Warwick warned of a potential new wave of COVID infections and deaths if coronavirus restrictions are relaxed before sufficient immunity has been achieved through the UK's vaccination programme.
The Daily Telegraph reported that their modelling suggests that, if vaccines provide an average 60% block on COVID transmission, then ending lockdown at the end of May and reverting to the coronavirus rules that were in place in early September produces the fewest deaths.
However, the newspaper added the experts suggested those restrictions - which included a ban on large events - would have to be maintained until the end of this year.
The Warwick paper was commissioned by SPI-M, a subgroup of the government's Scientific Advisory Group for Emergencies.
Asked about the modelling, Ms Truss told Sky News' Sophy Ridge On Sunday show: "I don't want to make predictions about the situation in the autumn.
"I think it's far too far away, but we have to take this on a step-by-step basis - opening up as we're able, making sure the most vulnerable are protected.
"That's the way to deal with this issue. Long-term predictions in what is a very, very unpredictable situation are not wise."
She said ministers were currently "putting our shoulders to the wheel" in their efforts to roll out COVID vaccines, with more than eight million people in the UK having received at least one dose of a vaccine.
Asked if the Warwick modelling was correct, Ms Truss added: "It's a long-term prediction. We need to take this on a week-by-week basis as we monitor what happens to the disease.
"The way to solve this is through global co-operation, it's through making sure we rollout the vaccine programme in the way we have been doing.
"It's making sure people are complying with the rules.
"That's what will help us get through this. I think speculating about what will happen in the autumn is far too far away."
Meanwhile, senior Conservative MP Jeremy Hunt reiterated his call for more government help for people ordered to self-isolate as a means of controlling the spread of new COVID variants from abroad.
The former health secretary, now the chair of the House of Commons' health committee, pointed to the example of the coronavirus response in places such as South Korea, Taiwan, Hong Kong and Singapore.
"They took the whole business of quarantining people who might be infectious much more seriously," he told Ridge.
"I think one of the big things we've got to look at is how we are much, much more effective to get people to isolate who we need to."
Highlighting how 40% of people asked to isolate by NHS Test and Trace don't actually do so, he added: "The single most important thing is to give people the confidence they're not going to be out of pocket financially.
"I think we do need to say to people, 'this is a public health matter, if you are out of pocket in terms of your salary while you're in that self-isolation period, the government will make up the difference'."
At present, only those on a low income who cannot work from home and receive one of seven means-tested benefits are eligible to claim a one-off £500 payment when self-isolating.
Former prime minister Tony Blair urged international leaders to consider a "common travel pass" to allow people to cross borders again.
"I think this is going to be inevitable in the end, the only way you are going to be able to get people travelling again is if they are able to prove either vaccination or testing status and do it by means that are verifiable," the Labour ex-premier told the programme.