UK ministers were warned that coronavirus cases could rise to more than a million per week before they lifted most of England’s restrictions.

Modellers made the gloomy suggestion in a paper on July 14, in which they said restrictions might have to return if cases did not level off.

The revelation came amid uncertainty over the current state of the outbreak in Britain, with the daily tally of cases falling but other data suggesting they are still rising.

A spell of warm weather, the end of football’s Euro 2020 championships and a reluctance among some people to get tested and face isolation have all been suggested as reasons for the apparent drop.

Scientists say it is too early to assess the impact of the unlocking in England on July 19, when masks became voluntary and limits on socialising were lifted.

The UK's devolved governments have their own health policies.

Ministers pressed ahead with the reopening despite the warning from modellers that a surge in cases could follow.

“If incidence reaches very high levels, such as greater than one million infections per week, there could be implications for workforces and critical infrastructure,” scientists on modelling advisory panel the Scientific Pandemic Influenza Group on Modelling, Operational sub-group said.

“If growth in incidence does not show signs of starting to plateau at expected levels … then stringent measures may be required to reverse growth.”

The most cases recorded in a single week were the 417,620 new infections added to the tally in one seven-day period in January.

In their statement of concerns, which was made public on Friday, the modellers expressed fears that September and October would be a “particularly risky point” in the trajectory of the pandemic.

This is because schools and universities will return and other seasonal infections could increase in prevalence, complicating the picture with Covid-19.

UK Prime Minister Boris Johnson argued when restrictions were lifted that it was better for a third wave to come in summer rather than autumn.

A record 689,313 people were told to isolate by the UK National Health Service’s contact-tracing app in the week to July 21.

There have been reports of people deleting the app to avoid being told to isolate, and scientists suspect that some people are not getting tested for the same reason.

Daily case numbers “depend on how many people turn up to be tested, and on why people are being tested”, said Prof Kevin McConway, a statistics expert at the Open University.

“The concerns about people being ‘pinged’ by the NHS Covid-19 app and having to self-isolate could be deterring some people from coming forward to be tested.”

'Chaotic' data

The seven-day average of new cases in Britain fell to 28,272 on Friday, a drop of 36 per cent in a week.

But the latest results from an infection survey by the Office of National Statistics showed cases in England continuing to rise.

The ONS survey is seen as reliable because it randomly samples the population, but it typically lags behind the government’s daily numbers.

“Overall, we are seeing chaotic datasets that reflect a lot of different things happening at the same time,” said Dr Simon Clarke, a microbiologist at the University of Reading.

Amid widespread chaos caused by the numbers of people isolating, key workers who are fully vaccinated have been exempted from isolation when alerted by the app.

This exemption will be extended from August 16 to anyone who is fully vaccinated.

Vaccination could become a condition of entry to venues such as nightclubs and football grounds, once everyone has had a chance to get two doses.

The question of whether to introduce vaccine passports in domestic life has been a cause of division and protest across Europe in recent weeks.

UK Transport Secretary Grant Shapps said it would be a good idea for companies to require employees returning to the office to be fully vaccinated.

He said the government would not legislate to make this compulsory but predicted that some companies would make it a requirement.

The prospect of a “no jab, no job” policy led to a warning from the UK’s Equality and Human Rights Commission that it should not lead to discrimination.

“Employers are right to want to protect their staff and their customers, particularly in contexts where people are at risk, such as care homes,” it said.

“However, requirements must be proportionate, non-discriminatory and make provision for those who cannot be vaccinated for medical reasons.”