The prime minister and chancellor are now self-isolating after contact with Health Secretary Sajid Javid, who has tested positive for coronavirus.
No 10 initially said they would not have to isolate, as they were taking part in a pilot scheme that involves daily testing instead.
But opposition parties said it suggested there was “one rule for them and another for the rest of us”.
The PM later said they had “briefly” considered taking part in the scheme.
It comes ahead of the lifting of lockdown rules in England from Monday.
Almost all legal restrictions are to end, including limits on how many people can meet, and nightclubs will reopen, but self-isolation rules will remain.
Following news that Mr Javid had tested positive and been in contact with Boris Johnson and Rishi Sunak, No 10 said a workplace pilot scheme would allow them to keep working from Downing Street.
But the announcement met with an angry response, with Labour’s Jonathan Ashworth saying it was unfair politicians appeared to have access to “VIP testing” to avoid self-isolation, while Liberal Democrat Leader Ed Davey asked if it was only available to the “privileged few”.
Speaking in a video on Twitter after the U-turn, Mr Johnson said: “We did look briefly at the idea of us taking part in the pilot scheme, which allows people to test daily, but I think it’s far more important that everybody sticks to the same rules and that’s why I’m going to be self-isolating until Monday 26 July.
“I know how frustrating it all is, but I really do urge everybody to stick with the programme and take the appropriate course of action when you’re asked to do so by NHS Test and Trace.”
The prime minister also defended the lifting of restrictions – amid ongoing rises in cases, deaths and hospitalisations – but urged people to be cautious.
He said: “We’ve got to remember that this virus is sadly still out there. Cases are rising. We can see the extreme contagiousness of the Delta variant, but we have this immense consolation and satisfaction that there is no doubt at all that the vaccine programme has very severely weakened the link between infection and hospitalisation and between infection and serious illness and death.”
Mr Johnson will now conduct meetings remotely from Chequers, the prime minister’s countryside retreat, where he was when the health secretary received his positive test result.
Mr Sunak said on Twitter: “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.”
Labour leader Sir Keir Starmer said infection rates were “going through the roof”, causing hundreds of thousands of people to have to self-isolate.
He told reporters: “What happens when the rules apply to the prime minister? He tries to wriggle out of them and to pretend that he’s on some pilot scheme that exempts him.
“I’m afraid yet again we see it’s one rule for them and another rule for everybody else.”
The managing director of the Iceland supermarket chain, Richard Walker, also criticised the proposal for Mr Johnson and Mr Sunak to avoid self-isolation.
“Shame the hundreds of Iceland staff who’ve been pinged can’t avoid self-isolation. We can all do a daily lateral flow test,” he said.
Mr Javid tested positive on Saturday morning after a meeting at Downing Street the day before, and both Mr Johnson and Mr Sunak were contacted by NHS Test and Trace. BBC news