Professor Ravi Gupta a member of the New and Emerging Respiratory Virus Threats Advisory Group (Nervtag), said that with the UK in the grip of an "early" third wave of Covid-19 infections, ministers should consider pushing back their target of scrapping all Covid measures on June 21 "by a few weeks".
The University of Cambridge academic said there had been an "exponential growth" in the number of cases, fuelled by the more transmissible Indian variant, but that the "explosive" impact it could have was currently being masked by the high vaccination rate.
More than 39 million people have been given a first jab and a further 25.3 million have had both doses.
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It comes as NHS chiefs warned that the lockdown-induced backlog of treatments for ailments other than Covid mean that even a small increase in the number of coronavirus patients could cause hospitals to be overstretched once again.
When asked about the possibility of a delay to freedom from restrictions, Environment Secretary George Eustice said nothing could be ruled out.
With both deaths and cases up significantly in the past week, experts are urging the Prime Minister to keep to his "data not dates" approach to easing lockdown.
Between May 24 and 30 there were 60 deaths reported within 28 days of a positive coronavirus test, an increase of 42.9% compared with the previous seven days.
Sunday also saw a further 3,240 lab-confirmed cases in the UK, with the number of cases between May 24 and May 30 - 22,474 - 26.8% higher than the previous seven days.
Prof Gupta told BBC Radio 4's Today programme: "It will probably take longer than earlier waves to emerge because of the fact that we do have quite high levels of vaccination in the population, so there may be a false sense of security for some time, and that's our concern.
"I think the problem is we are not too far from reaching the sort of levels of vaccination that would help us contain the virus and I think that people are not saying we should abandon the June 21 date altogether but just to delay it by a few weeks while we gather more intelligence and we can look at the trajectory in a clearer way.
"If you look at the costs and benefits of getting it wrong, I think it is heavily in favour of delay."
Leading scientific adviser Professor Adam Finn said a clearer picture was needed of the impact of the easements brought in this month before further relaxations take place.
Since May 17, two households or a maximum of six people from multiple households have been permitted to socialise indoors, including in pubs and restaurants.
Prof Finn, a member of the Joint Committee on Vaccination and Immunisation, said that while encouraging data has emerged in recent weeks over Covid hospital admissions in Britain, any impact on admissions brought by the easing of restrictions in May would not be known until "around about June 21 or just before that".
"I think it's unfortunate that everyone's got this particular date in their head, because really what we need to do is understand how things are going and adjust accordingly," he told ITV's Good Morning Britain.
"This time around, we should be cautious, wait to see what's happening, and then let everyone free, if you like, once we know for sure that that's safe and that we can do that without having another round of lockdowns and so on."
Cabinet minister Mr Eustice said the Government wanted to monitor the data before making a final decision on whether to go ahead with its June 21 plans to abolish social distancing and limits on socialising.
Pressed on whether businesses should prepare for a delay to the unlocking, Mr Eustice replied: "I've said all along, as has Matt Hancock and the Prime Minister, we can't rule anything out because we know this has been a difficult pandemic, a dynamic situation.
"We have to make that judgment a couple of weeks before.
"It will only be by then that we will see the full impact of the latest easements we made on May 17, so I know everyone wants to know what is going to happen but we can't actually make that judgment until we see the impact."
Chief executive of NHS Providers Chris Hopson said even a small uptick in severe cases was likely to hit the health service as it recovers from the winter-into-spring lockdown.
He told Times Radio: "The concerns are that this is a much more transmissible variant. We've still got lots of people still to vaccinate. And absolutely hospitals are very busy.
"We're talking to people who are saying 'We've got 96-97% bed occupancy, this is not the kind of bed occupancy we would normally expect at this time of year'.
"We're trying to go full pelt, to recover those care backlogs, we seem to be getting more people coming in on the urgent and emergency care pathway than we were expecting.
"So when you've got those volumes of patients, even small numbers of Covid-19 patients clearly add to the pressure."