The Prime Minister and the Chancellor had originally planned to take daily tests rather than self-isolate following meetings last week with Health Secretary Sajid Javid who has tested positive for Covid-19.
But in a dramatic turnaround, Downing Street said the two ministers would be self-isolating rather than taking part in a daily contact testing pilot.
“The Prime Minister has been contacted by NHS Test and Trace to say he is a contact of someone with Covid,” a spokesman said.
“He was at Chequers when contacted by Test and Trace and will remain there to isolate. He will not be taking part in the testing pilot.
“He will continue to conduct meetings with ministers remotely. The Chancellor has also been contacted and will also isolate as required and will not be taking part in the pilot”.
Mr Sunak said in a tweet: “Whilst the test and trace pilot is fairly restrictive, allowing only essential government business, I recognise that even the sense that the rules aren’t the same for everyone is wrong.
To that end I’ll be self isolating as normal and not taking part in the pilot.
Mr Johnson and Mr Sunak sparked outrage over their initial plans to not self-isolate.
Co-leader of the Green Party Jonathan Bartley said “anger doesn’t begin to cover it”.
Writing on Twitter Mr Bartley said: “Hundreds of thousands of young people, including my children, had their education and lives repeatedly turned upside down again and again after dutifully and responsibly isolating. And now this.
“Anger doesn’t begin to cover it.”
Liberal Democrat leader Sir Ed Davey said: “It is one rule for them and another rule for everyone else.
“How about the school teachers, transport workers and health workers getting a chance to be part of this test pilot or is it only for the privileged few?
“People have stuck to the rules and done the right thing, Boris Johnson is taking them for granted.”
Businesses have been pressing for the app to be overhauled and made less sensitive amid concerns that staff shortages mean they cannot operate effectively.
Steve Turner, assistant general secretary of Unite, said: “How are we meant to get this virus under control when those who set the guidelines don’t even follow them?
“My members at Nissan and thousands more across manufacturing, health, hospitality, retail and public transport live in fear of being pinged by the app as it means that they can’t work because they have to isolate.”