Ministers have been warned that the UK does not have the testing capacity to bring the "pingdemic" to an immediate end.
Senior sources close to the testing programme warned that if the Government brought forward a relaxation of the self-isolation rules, the system would not easily be able to meet demand.
"I cannot see how we would cope if everyone pinged by the app asked for a PCR test," one source told The Telegraph. "You’re talking about more than a million people, potentially. We’re already up against it, and at the moment the spare capacity simply isn’t there."
From August 16, people who have two jabs will be able to stop self-isolating after coming into contact with someone with Covid if they get a negative PCR test result. Currently, most people in such a position have to quarantine for 10 days.
Downing Street has so far resisted the demands. On Friday, George Eustice, the Environment Secretary, indicated that the date could even be put back, saying it could "always change in either direction".
A Number 10 source insisted testing capacity was not the reason the August 16 rule change was not being brought forward. The source cited instead a desire to get more people vaccinated and monitor changes in Covid cases in the wake of the recent lifting of restrictions.
However, concerns about testing capacity have been discussed by the Covid-O Cabinet committee, The Telegraph can reveal. A briefing paper circulated before a meeting of the committee on Thursday said: "Demand on testing, tracing and genomic sequencing could exceed capacity if cases rise beyond the level in SPI-M."
SPI-M is an acronym for the Scientific Pandemic Influenza Group on Modelling, which maps predictions on possible outcomes of the Covid pandemic to help policy-makers.
Even though the daily Covid case count has dipped in recent days, there are concerns in Whitehall that the dropping of almost all major restrictions earlier this week could trigger a new surge.
The limits of testing – both PCR and lateral flow tests – are closely linked to the debate about when self-isolation rules can change. One source said that last week ministers ordered more lateral flow tests amid fears they would "run out" by around mid-August. The availability of PCR tests is also coming under pressure.
Last week, the NHS admitted that turnaround times for testing in the community had "decreased substantially" since May. Official figures show that the percentage of tests processed within 24 hours fell sharply from 93 per cent in May to 64 per cent in the week ending July 14.
A testing source said turnaround times could fall even further if the change to self-isolation rules was brought forward. They warned this could push processing times beyond 72 hours, when samples can go off and produce false negatives.
In the spring, when cases were low, the Government scaled down testing capacity in the Lighthouse labs originally set up in the early months of the pandemic. One facility in Loughborough was closed down altogether.
Ministers had hoped that a new mega-lab – the Rosalind Franklin Laboratory in Leamington Spa – would be up and running in time to deal with any summer surge in cases. However, The Telegraph understands that only one line out of six at the lab is currently processing tests, with the facility operating at eight per cent capacity.
A Department of Health and Social Care spokesman said: "The testing and tracing being delivered across the country is saving lives every single day and stopping the spread of the virus by breaking chains of transmission and helping to control outbreaks wherever they exist.
"NHS Test and Trace has capacity in place to respond to increases in demand and people can have confidence that if they need a test, they can get one. Anyone who has Covid-19 symptoms can book home-testing PCR kits and more booking slots are made available at testing sites each day."