Mayor of London Sadiq Khan and business leaders have urged Boris Johnson to end self-isolation for contacts of Covid cases if they are fully vaccinated.
The PM is under growing pressure to replace the 10-day quarantine with daily testing for those alerted by the NHS Covid-19 app or Test and Trace.
It comes amid concerns of staffing shortages across sectors - including hospitality and the food supply chain.
The government plans to end isolation for those double-jabbed by 16 August.
But business leaders and cross-party politicians want the prime minister to bring forward the date - saying businesses are being put at risk by the "pingdemic".
In a letter to Mr Johnson, Mr Khan joined UK Hospitality, the London Chamber of Commerce and Industry and the capital's branch of the Federation of Small Businesses to demand change.
Nearly 608,000 contact tracing alerts were sent in England in the week between 8 and 15 July - a record high.
Hospitality businesses, such as pubs and restaurants, are struggling with staff shortages, causing some to close temporarily, the letter says.
"The summer months are crucial for many businesses' recovery and their ability to recover must not be put in jeopardy," it reads.
"We are therefore calling on you to ensure that the necessary testing is in place to enable people who have been double vaccinated for longer than two weeks and pinged by the NHS Covid app, to immediately return to work, following a negative PCR test, rather than having to self-isolate."
This would help employers and employees to retain faith in the NHS Covid-19 app in England and Wales, the signatories say.
Hospitality firms aren't the only industries to suffer staff shortages due to self-isolation - a number of railway companies have announced reduced timetables for the weekend or beyond.
Meanwhile, police, firefighters, Border Force staff, transport and freight workers will be able to join the daily contact workplace testing scheme, meaning they can avoid self-isolation if they are a contact of a Covid case.
The scheme was announced by the government on Thursday, initially for supermarket depots and food manufacturers.
But - separately to the mayor's letter - some in the food industry say the plan isn't enough.
British Frozen Food Federation chief executive Richard Harrow said workers may be freed up in some areas, such as factories, but not others, such as supermarkets.
"It shows that yet again government does not understand how connected the food supply chain is," he told the PA news agency.
"Only opening part is unlikely to solve the overall issue. Plus, who is in and who is out, who decides and how do they decide?
"Confusion continues to pervade and I have been advised no list until Monday. This is worse than useless."
Iceland managing director Richard Walker said he was "deeply disappointed to see supermarket store workers omitted from the list [of sectors that wouldn't need to isolate]".
Friday's daily figures showed Covid cases were down for the third consecutive day in the UK, with 36,389 new infections.