Caution is needed in determining whether England’s coronavirus restrictions can be lifted next month or the situation could turn bad “very, very quickly”, a professor whose argument against herd immunity helped trigger England’s first lockdown has warned.

Sir Tim Gowers, Professor of Mathematics at the University of Cambridge, told The Guardian the downside of being “a bit more cautious” was a lot smaller than the downside of getting it wrong.

Asked about the next step in lockdown easing in England, due on June 21, Prof Gowers said he did not believe the plans were necessarily at risk, but urged caution.

“Because Boris Johnson has made a big thing about all the steps being irreversible, I think he’s put himself in a position where once he takes a step, he’ll be extremely reluctant to reverse because that would be a big U-turn, an embarrassing climbdown,” he said.

“So I think if that’s the way you’re going to play things, then you should be very, very cautious about every step you take … And maybe everything [will] be OK, maybe the number of people who are vaccinated will be just enough … ‘R’ will broadly speaking stay below one even with Indian variants.

“But if it’s not OK, we know, because of mathematics, that things will get bad very, very quickly. Or at least, maybe it won’t look that quick to start with, but it’ll grow exponentially.

“So it’ll pick up speed and become a big problem.”

The Guardian said Prof Gowers sent the Prime Minister’s former chief adviser Dominic Cummings a five-page document warning of the need to “move urgently to extreme containment measures” in March last year.

Other experts on Friday argued restrictions should remain in place until more of the population had received both vaccine doses. Professor Christina Pagel, a member of Independent Safe from University College London, said reopening should be delayed a few more months.

The Prime Minister told reporters on Thursday he “didn’t see anything currently in the data” to divert from the June reopening target before adding: “But we may need to wait.”

The Times reported face coverings and work from home guidance may remain in place after June 21, when all legal limits on social contact are due to be lifted in England.

It said ministers were increasingly concerned the spread of the Indian variant could undermine the easing of restrictions and were drawing up plans that could lead to a partial end of lockdown.

But the paper added the Treasury was prioritising the removal of the “one-metre plus” and “rule of six indoors” measures in order to help the economy recover.

A review of what measures will be relaxed on June 21 was due by the end of May but has been pushed back due to the Indian variant.

Meanwhile, a Joint Committee on Vaccination and Immunisation (JCVI) source told The Daily Telegraph it is expected to set out “options and consequences” of vaccinating children rather than offering a firm recommendation for ministers to follow.

The source said: “It’s likely that the JCVI will come up with a menu of options saying what the consequences of each of them would be, rather than making an actual recommendation.”

Their comments come after the European Medicines Agency recommended the use of the vaccine made by Pfizer and BioNTech be expanded to children aged 12 to 15.

A single-shot coronavirus vaccine from Johnson & Johnson has also been approved for use in the UK and should be available towards the end of the year.

The vaccine is part of the UK’s Cov-Boost study which is examining the effectiveness of a range of vaccines that could be used as a booster shot in the autumn.

The Department of Health and Social Care announced on Friday further surge testing was being deployed in Lancashire after more cases of the Indian variant were detected.

People living, studying and working in areas including Burnley, Pendle, Hyndburn and Rossendale are being urged to take a PCR test even if they do not have symptoms, while additional mobile testing units and Covid-19 tests are being deployed to higher educational settings.

Current data suggests although hospital admissions are rising in some parts of the country affected by the Indian variant, overall admissions remain broadly flat.

Data for England published on Friday by the Office for National Statistics shows an estimated one in 1,120 people in private households had Covid-19 in the week to May 22 – broadly unchanged from one in 1,110 in the previous week. The estimate for Scotland is around one in 630, up from one in 1,960, putting Scotland back to where it was around a month ago.

Meanwhile, the reproduction number – the R value – for England is 1 to 1.1, up from 0.9 and 1.1 the previous week, suggesting the epidemic is growing.

The latest seven-day average for daily hospital admissions in England is 88 (up to May 25), which is an increase of 15% on seven days earlier.

The figure means hospital admissions are back to where they were at the start of May and remain 98% below the second-wave peak in January.

Public Health England data shows the majority of people with the Indian variant have not been vaccinated, with just 3% of cases (177 out of 5,599) from February 1 to May 25 having received both doses.

Over the period there were 12 deaths linked to the variant, of which eight were among the unvaccinated.

Dr Mike Tildesley, from the University of Warwick and a member of the Scientific Pandemic Influenza Group on Modelling (Spi-M) group, told the BBC that cases would go up but the vaccines are proving helpful.

He said experts needed to “gather as much evidence as we can over the next week or two” then “try to predict what we expect may happen should this June 21 relaxation go ahead”.