Prof Robert Dingwall, a sociologist who is a member of the New and Emerging Respiratory Virus Threats Advisory Group (Nervtag), said "from a societal point of view, I think it’s really important that we go ahead on 21 June".
He said there is “no case for delay” given, for example, the backlog of treatments needed for non-COVID health conditions and continued damage lockdown is inflicting on the economy.
But his comments on Tuesday were completely at odds with another Nervtag member, Prof Ravi Gupta, who said the 21 June target date to lift all restrictions on social contact should be scrapped.
He called for the end of lockdown to be delayed until July.
Nervtag, which consists of 19 professors and doctors, advises the government on the threat posed by respiratory viruses such as COVID-19, and provides options on how to manage them.
The 21 June target date has been complicated by the more transmissible B.1.617.2 “Indian” variant. On Thursday, Public Health England announced cases had doubled in the space of a week to nearly 7,000.
Overall COVID cases have been above 3,000 a day for the past six days, meanwhile.
However, Prof Dingwall, speaking on Times Radio, said everyone in the top nine priority groups will have been offered a vaccine by 21 June, and that COVID for younger age groups is a “mild illness”.
Watch: Daily politics briefing: 1 June
“There is no realistic prospect of the NHS facing the sorts of pressures that it faced in January and February. And that’s why I think we have to we have to push on with this.”
He added the current “wave” of infections is a “preview” of what life will be like in the years to come.
“These waves will come, they will pass through, there will be high levels of mild infections in the community for periods of time, a handful of people may be seriously ill, even fewer may die.
“But that’s what happens with respiratory viruses.”
Prof Gupta, on the other hand, said the end of lockdown should be delayed “by a few weeks” as it’s still too early “to put the vaccine straight up against the virus”.
As of Sunday, the latest day for which figures are available, 74.8% of UK adults had received a first dose, with 48.5% having had both doses.
Boris Johnson announced the “road map” out of lockdown on 22 February, and Prof Gupta told ITV’s Good Morning Britain: “We didn’t plan for the B.1.617.2 variant when the initial roadmap was made, and actually things have gone really well except for the fact that we have this new variant to complicate things.
“We must remember this is a virus that does adapt, and faced with vaccines it will eventually start to make mutations to avoid them even further, and then we could be in an even more precarious situation after that.”
Speaking on BBC Breakfast, meanwhile, the government’s former chief scientific adviser Sir Mark Walport was somewhere in between the two sides of the argument.
Sir Mark said it’s “not impossible” the UK could be at the beginning of a third wave, and that the nation is in “a quite perilous moment”.
However, he also pointed out hospital admissions “are not surging – if anything they’re coming down”.
The prime minister is expected to make an announcement about the end of lockdown on 14 June.
Later on Tuesday, a Downing Street spokesman indicated Johnson still sees nothing in the data to suggest the unlocking date will be put back.
Asked about the PM's current plans amid warnings over the Indian variant, the spokesman said: “The prime minister has said on a number of occasions that we haven’t seen anything in the data but we will continue to look at the data, we will continue to look at the latest scientific evidence as we move through June towards 21 June.”
Watch: Monday's vaccines in numbers