Mass testing could see people given a “freedom pass” to go about life as normal, safe in the knowledge they are not infectious with Covid-19, the Prime Minister has said.

Expanding on plans for so-called Operation Moonshot, Boris Johnson said that millions of people could be tested every day so they could “behave in a way that was exactly as in the world before Covid”.

Theatres and sports venues could test all audience members and let in those with a negative result, the Prime Minster said at a Downing Street briefing.

Trials with audience members are to be run in indoor and outdoor venues in Salford from next month, he said, with a hope to go nationwide.

“We’re hoping the ‘Moonshot’ approach will work and we will be able to deliver mass testing which will give people the freedom pass, the ‘laissez-passer’, the knowledge that they are not infectious and can hang out with other people who are not infectious in a pre-Covid way,” he said.

But the proposals come as the current testing programme faced considerable criticism for struggling to meet demand.

Many people who tried to access a test on Wednesday were met with the error message telling them to try again and warning them not call the helplines.

And on Tuesday the NHS Test and Trace director of testing apologised to people who were unable to get a test.

The mass testing proposals were outlined as the Prime Minister, the Health Secretary and England’s chief medical officer all implored people not to get a test if they did not need one.

Professor Chris Whitty admitted there were “constraints” in the system, adding “It’s critical that those who do need to be tested, and in particular people with symptoms or people who have been told to for a variety of reasons, social care working for example, get tested.

“But it is also important that people who really don’t have a clear clinical indication currently don’t (get tested) because we do still have constraints.

“Those constraints are not just going to magically disappear, and the demand on testing has increased.”

Matt Hancock said there had been an increase in people seeking tests when they have not got symptoms of Covid-19.

Mr Johnson also reiterated the plea: “If you don’t have symptoms, and you haven’t been asked to book a test, please don’t.”

Free tests are available to people with symptoms of coronavirus – a fever, new and continuous cough or a loss or change in sense of taste or smell – and for some other people, such as those who have been instructed to do so by a doctor or local council and some essential workers.

Mr Johnson said the mass-testing plans could “allow life to return to closer to normality”.

He said: “We’re working hard to increase our testing capacity to 500,000 tests a day by the end of October.

“In the near future we hope to start using testing to identify people who are negative, who don’t have coronavirus, who are not infectious. So we can allow them to behave in a more normal way in the knowledge they can’t infect anyone else with the virus.

“And we think, we hope, we believe that new types of tests which are simple, quick and scaleable will become available and they use swabs, or saliva, and can turn around, results in 90, or even 20 minutes.

“Crucially, it should be possible to deploy these tests on a far bigger scale than any country has yet achieved, literally millions of tests, being processed every single day.

“That level of tests would allow people to lead more normal lives without the need for social distancing.

“Theatres and sports venues could test an audience. All audience members, one day, and let in all those with a negative result, all those who are not infectious

“Workplaces, could be opened up to all those who test negative in the morning to behave in a way that was exactly as in the world before Covid.

“And those isolating because they are a contact, or quarantining after travelling abroad could, after a period, be tested and released.

“Now that’s an ambitious agenda we’ll get to pilot this approach in Salford from next month with audiences in indoor and outdoor venues, and then we hope to go nationwide.”

He admitted that that the “Moonshot” plan faces “challenges” including manufacture, logistics and technology issues.

“We’re hopeful this approach will be widespread by the spring, and if everything comes together it may be possible for some of those difficult sectors like theatres to have life much closer to normal before Christmas.”

He said with daily testing where everyone would get a “pregnancy style” rapid turn around test in the morning and 15 minutes later they would know whether or not they were infectious, which would give them a “freedom pass” to meet with others.

A briefing memo sent to the first ministers and Cabinet secretaries in Scotland, seen by The BMJ, says that the UK-wide Moonshot programme is expected to “cost over £100bn to deliver”.

Separate information, also seen by The BMJ, suggests this will include plans for 10 million tests to be processed each day.