Delaying the easing of self-isolation rules for coronavirus contacts until a month after England’s other restrictions are lifted is “not a perfect solution”, a Cabinet minister has admitted.

Business Secretary Kwasi Kwarteng insisted the Government has to strike a balance between reopening the economy and curbing the spread of Covid-19, as ministers faced a backlash over the plans.

From August 16, people in England who have received both doses of a vaccine – as well as the under-18s – will no longer have to self-isolate if they have been in contact with someone who tests positive for Covid-19.

But restrictions on businesses and social gatherings will be removed at Step 4 of the road map, expected on July 19, raising fears that increased cases could lead to millions being forced to spend 10 days at home.

Hospitality chiefs said the delay could lead to staff shortages, warning that the current system is already causing “carnage” and unless the Government moves quicker it risks “the summer being cancelled and vast swathes of the population unnecessarily confined to their homes”.

Kate Nicholls, boss of trade body UKHospitality, said: “With cases predicted to continue to rise, this means that hospitality’s recovery after 16 months of lockdown and severely disrupted trading will be harmed.”

Former Tory leader Sir Iain Duncan Smith said: “Why would you even go to a pub (after July 19)? This makes it worse.”

He told the Daily Telegraph: “I wouldn’t go to a pub that wasn’t still having six around a table and social distancing, otherwise you run the risk of everyone in the pub being pinged and locked down.”

But the Business Secretary told Sky News: “You can’t have it both ways. On the one hand we’re saying we want to reopen, but we’re giving a measure of precaution in terms of delaying the lifting of self-isolation restrictions.

“It’s a balance, it’s not a perfect solution. But on the one hand we’re saying that we can reopen and on the other we’re saying that we want to give a little bit more protection in terms of the self-isolation rules.”

Health Secretary Sajid Javid has warned there could be 100,000 cases a day by the summer, something which free market think tank the Adam Smith Institute predicted would result in 3.5 million people a week being forced to self-isolate.

But the think tank’s projections were for an even higher level of daily infections, up to 133,000 by August 4, which would result in 4.6 million a week self-isolating.

However, Mr Kwarteng played down that prospect, saying: “I don’t think you can necessarily conclude there will be millions.”

Asked if there could be a change to the timetable, Mr Kwarteng told BBC Radio 4’s Today programme: “I think we have to assume that this is it.

“But, as I always say in these things, we’re looking at data in real time.”

Professor Christophe Fraser, from Oxford University’s Nuffield Department of Medicine, who advises NHS Test and Trace, told Times Radio: “At the moment the epidemic is growing exponentially; we know that exponential (growth) very rapidly leads to big numbers – we’re two doublings away from 100,000 cases a day. And the doubling rate has been consistently between nine and 11 days so that’s not a lot of time ahead.

“And we don’t know when that’s going to peak – the different models have different projections, there’s considerable uncertainty at what stage the epidemic is going to peak.”

He added that 100,000 cases a day “would result in a large amount of people being traced”.

Meanwhile, Heathrow is to provide fast-track lanes for fully-vaccinated arrivals as the airline industry steps up pressure on ministers to open up quarantine-free travel to amber destinations.

Under a pilot programme to be launched this week, passengers from selected destinations will be able to upload their coronavirus vaccination certificate before boarding.

On arrival at the airport, they will then be directed to dedicated lanes at the border to speed their passage through immigration.

This pilot will allow us to show that pre-departure and arrival checks of vaccination status can be carried out safely at check-in, so that fully-vaccinated passengers can avoid quarantine from July 19

The move comes ahead of an expected announcement on Thursday when Transport Secretary Grant Shapps will set out details of the Government’s plans to end the requirement for travellers from amber list countries to self-isolate on arrival.

Boris Johnson is said to favour easing the controls from July 19 – in line with Step 4 – according to The Times.

Heathrow, together with British Airways and Virgin Atlantic – the two airlines involved in the trial programme – said it is essential that there is no delay in implementing the changes.

The scheme will initially involve fully-vaccinated volunteers travelling on selected flights from Athens, Los Angeles, Montego Bay in Jamaica, and New York.

Heathrow chief executive John Holland-Kaye said: “This pilot will allow us to show that pre-departure and arrival checks of vaccination status can be carried out safely at check-in, so that fully-vaccinated passengers can avoid quarantine from July 19.”