The Cambridge professor whose argument against a herd immunity strategy helped trigger England’s first lockdown has voiced concerns about the risks of easing restrictions next month. Prof Sir Tim Gowers sent Dominic Cummings a five-page document warning of the need to “move urgently to extreme containment measures” in March last year. Boris Johnson’s former chief aide told MPs this week it had influenced a critical change in the government’s early thinking, with lockdown announced two days later. In an interview with the Guardian, Gowers said “things will get bad very, very quickly” after 21 June – the fourth and final lockdown-lifting step – if the government had misjudged factors such as the spread of new Covid variants. As UK Covid cases rose by 4,184 on Friday – the highest increase since 1 April – Gowers added: “The downside of being a bit more cautious is quite a lot smaller than the downside of getting it wrong.” Gowers, a world-leading mathematician and winner of the Fields Medal – sometimes described as the Nobel prize of maths – was described by Cummings as “one of the smartest people on the planet” during evidence to two parliamentary committees. Discussing the delayed decision to lock down in March 2020, which has been linked to 20,000 avoidable deaths, Cummings said Gowers’ argument was among key interventions that meant he “finally had the confidence to say [to Boris Johnson] that I thought that the system had gone catastrophically wrong” last year. His evidence to MPs, and Gowers’ latest comments, come amid fears that the spread of the Covid variant first identified in India could trigger a rise in cases, hospitalisations and deaths. On Thursday, Public Health England revealed that the variant accounts for up to 75% of new reported cases across the UK, with numbers doubling in a week. From 21 June, the government hopes to “remove all legal limits on social contact” in England, reopening nightclubs and easing restrictions on large events including weddings, though Johnson warned on Thursday that “we may need to wait”. Asked about the next step in lockdown-easing, Gowers said he did not necessarily believe the lockdown easing plans were 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.” Gowers was speaking to the Guardian after Cummings told how he had shared documents from the government’s Scientific Advisory Group for Emergencies (Sage) with a select group of people in March as he agonised over whether Downing Street should initiate its first lockdown. Until this point, Cummings said, the government had been following a strategy of herd immunity – allowing people to catch Covid to boost the number with antibodies – though this is denied. By the evening of 13 March, Cummings said, he had realised he needed to tell Johnson that the plan had to be ditched to avert the biggest health disaster since the first world war. Meanwhile, Gowers said he could precisely date the moment at which he realised that a herd immunity policy was “disastrously wrong”. After writing a Twitter thread on 13 March in which he backed the concept, a reply prompted him to re-evaluate. “I did a very simple back-of-envelope calculation which made it clear that the stated aim of achieving herd immunity by the autumn would require far more people to be hospitalised than the NHS could conceivably cope with,” he recalled. In a second thread, he “disowned” his sympathetic account of the strategy from a few hours earlier and explained why achieving herd immunity by the autumn without overwhelming the NHS was clearly impossible. “It’s good that I came to that realisation when I did, because the day after that (or to be precise at 1.23am, but I saw it only when I got up the next morning), Dominic Cummings, who already knew me from discussions about mathematics teaching several years ago, got in touch. So I wrote and told him that I thought we needed to move urgently to extreme containment measures.” He explained the mathematics in a document which he sent to Cummings and which is being published by the Guardian. It warned that the NHS did not have resources to implement a herd immunity policy “in a non-disastrous way” and pointed out problems surrounding a scenario in which 60% of people (40 million) would need to catch the coronavirus – a figure cited by the chief scientific adviser, Sir Patrick Vallance – for the strategy to be effective. “The most serious problem with the herd immunity policy, it seems to me, is that we can’t infect 60% of the population in a matter of months without overwhelming the hospitals and having to let a very large number of people die untreated,” Gowers’ document warned. On the question of how many of the 60% would need hospital treatment, it said that even “a very optimistic figure of 2%” meant 800,000 would need intensive care for the policy to work. Urging caution, Gowers said he hoped that the influence of Sage experts would outweigh pressure on the prime minister from Conservative MPs to lift all restrictions. While Sage had got things “a bit wrong” back in March 2020, they were “not making the same mistake twice” in September, he said. “I don’t know what advice Johnson is getting from Sage at this point. If he departs from their advice, then I would be very worried.” Gowers, 57, told how he and his family had started to implement their own form of social distancing and lockdown last year even before the official one was imposed. It was at this point that Cummings, who he had known from when the aide worked for Michael Gove at the Department for Education, reached out to him.