The lateral flow tests – which can provide results in around 30 minutes – will be available from Friday, regardless of whether people have symptoms.
The announcement comes as Boris Johnson is due to meet senior ministers on Monday to sign off the next stage of the road map out of lockdown.
People will be able to obtain a test through a home ordering service, workplace or school testing programme, or by collecting one at a local test site.
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The Prime Minister said the scheme would help stop fresh outbreaks, enabling the authorities to identify and control new variants of the disease.
“As we continue to make good progress on our vaccine programme and with our road map cautiously easing restrictions under way, regular rapid testing is even more important to make sure those efforts are not wasted,” he said.
“That’s why we’re now rolling out free rapid tests to everyone across England – helping us to stop outbreaks in their tracks, so we can get back to seeing the people we love and doing the things we enjoy.”
Mr Johnson will chair a virtual meeting of the Covid O committee before briefing the full Cabinet on the arrangements for the latest phase of lockdown lifting which will see non-essential shops in England reopen from April 12.
He will then set out the details at a Downing Street news conference where he is expected to say more about plans announced at the weekend for Covid certificates for mass gatherings from sporting events to nightclubs.
He will also outline the Government’s approach for lifting restrictions on holidays abroad starting from May 17.
Under the Government’s road map, pubs and restaurants will be able to start serving customers outdoors from next week while hairdressers, nail salons, gyms and libraries – as well as non-essential retail – will be able to reopen.
While there is relief among MPs at the prospect of the economy reopening, there is concern among some about the proposals for the “Covid status certification” scheme dubbed “vaccine passports”.
Ministers insist the certificates – which could be a mobile phone app or a paper document – will never be required for essential services such as supermarkets, public transport or GP surgeries.
Initially, at least, they will also not be necessary to go to pubs or restaurants as they begin serving again.
Ministers believe the scheme will be most useful in managing the risks where there are large numbers of people in close proximity such as music festivals, sporting matches and nightclubs.
However more than 40 Tory MPs have signed a cross-party letter opposing vaccine passports while Labour leader Sir Keir Starmer has described them as “un-British”, raising the prospect of a potential Government defeat if – as expected – there is a Commons vote.
Writing in The Daily Telegraph, Sir Graham Brady, the influential chairman of the backbench Tory 1922 Committee, said vaccine passports were “intrusive, costly and unnecessary”.
Under the plans set out at the weekend the certificates are expected to show whether an individual has received the vaccine, has recently tested negative for the virus, or has “natural immunity” having tested positive in the previous six months.
The Government is planning trials at a series of events over the coming weeks including the World Snooker Championship at the Crucible Theatre in Sheffield and culminating with the FA Cup final at Wembley on May 15.
Initially they will not involve the use of certificates although spectators will be required to be tested for Covid-19 both before and after the event.
Mr Johnson will also use the news conference – a year to the day after he was admitted to hospital with Covid-19 – to set out further details of the framework for easing foreign travel restrictions ahead of the report of the global travel task force, which is due on April 12.
While the ban on foreign travel from England will not be lifted until May 17, Downing Street has said that when the rules are relaxed there will be a risk-based “traffic light” system with red, amber and green ratings for countries around the world.
Travellers arriving from countries rated green will not be required to isolate although pre-departure and post-arrival tests will still be needed.
For those classed as amber or red, the restrictions will remain as they are with arrivals required to isolate or enter quarantine.
Officials have made clear that there will be no announcement this week on which country is on which list – a decision which has been criticised by tourism industry bosses.
Martyn Sumners, executive director of the Association of Independent Tour Operators, told The Times: “The fact that we won’t know until next month which countries are permitted for travel will make it very difficult to get programmes up and running.”
Hairdressers and barbers can reopen in Scotland from Monday, a week earlier than in England.
Some non-essential shops can also reopen, including garden centres and homeware stores, while university and college students will return for in-person teaching and outdoor contact sports can restart for youngsters aged 12 to 17.