Any relaxation of lockdown measures could trigger an exponential rise in coronavirus cases, government scientific advisers have warned ministers amid a cabinet split about how quickly to ease restrictions.

Quick guide Will there be a second wave of coronavirus? Show Hide In recent days the UK has seen a sudden sharp increase in Covid-19 infection numbers, leading to fears that a second wave of cases is beginning. Epidemics of infectious diseases behave in different ways but the 1918 influenza pandemic that killed more than 50 million people is regarded as a key example of a pandemic that occurred in multiple waves, with the latter more severe than the first. It has been replicated – albeit more mildly – in subsequent flu pandemics. Until now that had been what was expected from Covid-19.

How and why multiple-wave outbreaks occur, and how subsequent waves of infection can be prevented, has become a staple of epidemiological modelling studies and pandemic preparation, which have looked at everything from social behaviour and health policy to vaccination and the buildup of community immunity, also known as herd immunity. Is there evidence of coronavirus coming back in a second wave? This is being watched very carefully. Without a vaccine, and with no widespread immunity to the new disease, one alarm is being sounded by the experience of Singapore, which has seen a sudden resurgence in infections despite being lauded for its early handling of the outbreak. Although Singapore instituted a strong contact tracing system for its general population, the disease re-emerged in cramped dormitory accommodation used by thousands of foreign workers with inadequate hygiene facilities and shared canteens. Singapore’s experience, although very specific, has demonstrated the ability of the disease to come back strongly in places where people are in close proximity and its ability to exploit any weakness in public health regimes set up to counter it. In June 2020, Beijing suffered from a new cluster of coronavirus cases which caused authorities to re-implement restrictions that China had previously been able to lift. In the UK, the city of Leicester was unable to come out of lockdown because of the development of a new spike of coronavirus cases. Clusters also emerged in Melbourne, requiring a re-imposition of lockdown conditions. What are experts worried about? Conventional wisdom among scientists suggests second waves of resistant infections occur after the capacity for treatment and isolation becomes exhausted. In this case the concern is that the social and political consensus supporting lockdowns is being overtaken by public frustration and the urgent need to reopen economies. However Linda Bauld, professor of public health at the University of Edinburgh, says “‘Second wave’ isn’t a term that we would use at the current time, as the virus hasn’t gone away, it’s in our population, it has spread to 188 countries so far, and what we are seeing now is essentially localised spikes or a localised return of a large number of cases.” The overall threat declines when susceptibility of the population to the disease falls below a certain threshold or when widespread vaccination becomes available. In general terms the ratio of susceptible and immune individuals in a population at the end of one wave determines the potential magnitude of a subsequent wave. The worry is that with a vaccine still many months away, and the real rate of infection only being guessed at, populations worldwide remain highly vulnerable to both resurgence and subsequent waves. Peter Beaumont, Emma Graham-Harrison and Martin Belam

With Boris Johnson still recuperating at Chequers, his senior ministers have been at loggerheads over whether the public health and economic impact of the lockdown will soon begin to rival the consequences of the virus itself.

Rishi Sunak, the chancellor, Michael Gove, the Cabinet Office minister, and Liz Truss, the trade secretary, are known to be among those raising concerns about the impact of a lengthy shutdown on the economy, and on health conditions outside of coronavirus, since excess deaths from other causes appear to have risen too.

But other ministers appear to have taken on board the latest evidence from the Scientific Advisory Group for Emergencies (Sage), combined with Johnson’s own caution, and rowed back from initially hawkish positions on when schools and some businesses can return to normal.

Those whose positions are thought to have softened in recent days include Gavin Williamson, the education secretary, and Alok Sharma, the business secretary.

On Monday the reported death toll in UK hospitals rose by 449 – the lowest daily total for some time – and Angela McLean, the government’s deputy chief scientific adviser, said the figures were “pretty much stable and flat”, raising hopes that the UK could have passed its peak.

However, one cabinet source said the government’s advisers on Sage had presented the case that not a single loosening of measures could be undertaken soon without pushing up the rate of transmission for each person infected, known as R – and not enough data existed to say when it would be safe to do so.

The source said: “The scientists are very clear. There’s no loosening of measures we can do that won’t bring the R back over 1. There may be some small changes on their own that could do it, but the question is whether behaviours change in other ways and push the R above 1. The second you have the R above 1 then you’re back to exponential growth.

“We did have an R of about 3. And we’ve driven that down. But even a small increase in transmission could put you above 1.”

Even small changes, such as allowing more activities in parks or reopening some retailers, could increase the transmission rate too much, they said.

Johnson is not working while he recovers from his stint in intensive care, but is receiving updates on the crisis and is on the side of those concerned about stopping a second peak. Matt Hancock, the health secretary, is firmly in the same camp as the prime minister, arguing that the transmission rate has to be brought down to a very low level before the lockdown can be eased.

It makes Hancock the most strongly in favour of ensuring the spread of the virus is suppressed out of the key decision-making quad that also comprises Gove, Sunak and Dominic Raab.

Raab, the foreign secretary, who is deputising for the prime minister, is known to be instinctively very mindful of the economic consequences of the lockdown, but also very supportive of the argument that lifting the measures too soon could lead to a disastrous second peak.

Other key cabinet ministers – Sharma and Williamson – have been reportedly keen that the lockdown should be eased, but appear to have pivoted more towards caution in recent days. In an internet seminar last Friday, hosted by the CBI, Sharma echoed the prime minister’s position that lifting the lockdown too early could bring further setbacks to business because of a second peak of the illness, and said “that’s the worst possible thing you could do”.

In public, both Gove and Sunak have been careful to back the No 10 position that the lockdown is necessary for some while yet. Sunak told the daily No 10 press conference on Tuesday that “we can’t have the risk of a second peak. That would not only be bad for health outcomes, it would also be bad for the economy”.

However, multiple Whitehall sources confirmed that Sunak and Gove are on the hawkish side of the spectrum about lifting restrictions.

One government adviser told the Guardian that new conversations are now going on about the public health risks of an extended lockdown. The source said: “There’s a general feeling that we have been completely public health-guided but lockdown is not without its public health consequences as well. The increase in domestic abuse and also the established statistics show that whenever there is a recession, people die.

“There’s a discussion now saying of course we want to see that [science] but remember that if we stay locked down, this is having vital real-life consequences as well and we can lose thousands of lives through recession too.”

Gove is now leading a strategic unit in the Cabinet Office about the possible routes to easing physical distancing restrictions, but nothing is likely to be decided until Johnson is back at work. One paper under discussion is about the possibility of a traffic light system, whereby some shops could open in the red phase, car journeys and wearing of face masks would happen in the amber phase, and only in the green phase could mass gatherings restart.

Downing Street sources played down the significance of the traffic light paper, saying many options were being considered. Before ministers can finalise a plan for easing the lockdown, they will need to have put in place an infrastructure for stopping further spread of the virus.

Jeremy Hunt, the former health secretary, warned on Monday that contact tracing “needs to be our next national mission” in addition to greater testing capacity. Hunt, who is chairman of the health select committee, said a national figure outside of politics was needed to spearhead contact tracing, adding: “I hope we will get a move on so the cabinet has a choice to the current national lockdown when they come to review this decision in three weeks’ time.”

A major report by the Organisation for Economic Co-operation and Development (OECD) also said on Monday that testing and contact tracing in the community is the “most promising approach” in the short term to help lift the lockdown. The study said isolating people with coronavirus and tracing their contacts so they also isolate – an approach abandoned by the UK early on – is the key to controlling further outbreaks.