Boris Johnson and six Tory MPs he met at Downing Street last Thursday are self-isolating, after one MP later tested positive for Covid-19.
Ashfield MP Lee Anderson lost his sense of taste the day after the breakfast meeting at No 10.
On Sunday, the prime minister was told to self-isolate by NHS Test and Trace.
In a video on Monday, Mr Johnson urged others to “follow the rules” if contacted by the system.
A test-and-trace clinician spoke to Mr Anderson about his movements and decided his meeting with the PM counted as close enough contact to require self-isolation.
Mr Johnson, who was admitted to intensive care with coronavirus seven months ago, spent about 35 minutes with Mr Anderson and has maintained the pair followed all social distancing advice during the appointment.
The five others self-isolating following the meeting with “Red Wall” Tory MPs include:
The PM’s period of isolation begins as the government prepares a policy relaunch.
Downing Street said a series of “critical announcements” would this week detail Mr Johnson’s “ambitions for the United Kingdom”.
Mr Johnson will chair “key Covid meetings” and work with Chancellor Rishi Sunak to devise the upcoming spending review with an aim to fulfil his promise to “build back better”.
Health Secretary Matt Hancock will hold a No 10 news conference later, which the prime minister had been expected to lead.
The new policy plans follow the dramatic departure of the PM’s chief adviser Dominic Cummings last week.
Speaking on BBC Breakfast, Mr Hancock said the prime minister’s self-isolation would make no difference to the amount of work he would be able to do “driving forward the agenda”.
Asked if the PM and Mr Anderson followed social distancing rules during their meeting, he said there were rules “around Downing Street being a Covid-secure workplace”.
He added: “The central point is that it doesn’t matter who you are, if you are contacted by NHS Test and Trace and told to self-isolate that is what you must do.”
In the video, the PM added: “The good news is that NHS Test and Trace is working ever-more efficiently, but the bad news is that they’ve pinged me and I’ve got to self-isolate because someone I was in contact with a few days ago has developed Covid.
“It doesn’t matter that we were all doing social distancing, it doesn’t matter that I’m fit as a butcher’s dog, feel great.
“And actually, it doesn’t matter that I’ve had the disease and I’m bursting with antibodies. We’ve got to interrupt the spread of the disease and one of the ways we can do that now is by self-isolating for 14 days when contacted by Test and Trace.”
It remains unclear what effect, if any, previously having the coronavirus has on a person’s immunity but experts think reinfection is likely to be rare, BBC health correspondent James Gallagher has reported.
Speaking on BBC Radio 4’s Today programme, Danny Altmann, professor of immunology at Imperial College London, said there have been more than 25 confirmed cases of Covid-19 reinfection globally.
He added: “I think most of us think the rate of reinfection is quite a lot higher than that, but not enormous.”
Self-isolation means staying at home and not leaving it – even to buy food, medicines or other essentials, or for exercise.
If you are told to self-isolate by NHS Test and Trace or the NHS Covid-19 app, you must self-isolate for 14 days from the day you were last in contact with the person who tested positive for coronavirus.
And if you develop symptoms during the 14 day period, you should get a test as soon as possible.
If the result is negative, you should continue isolating for the rest of the 14 days.
If positive, you should self-isolate for at least another 10 days from when your symptoms started.
On Thursday, Mr Anderson, the Conservative MP for Ashfield, posted a photo of himself with Mr Johnson at No 10 alongside the words: “Breakfast with the PM.”
On Sunday, he posted on his Facebook page to say he was self-isolating with his wife, who is clinically vulnerable, after they both tested positive.
The PM wrote on Twitter on Sunday night that he had been notified by NHS Test and Trace that he must self-isolate as he had been in contact with someone who tested positive, and he would be working from No 10.
Boris Johnson will now have to stay at home in No 10.
It means he will not be able to be in Parliament, though I’m told he will be working from Downing Street.
He does still intend to keep communicating with the country.
It was supposed to be a pretty big week for Boris Johnson – he is trying to reset his government after some factional fighting in his office over the last few days.
There are conversations taking place with the parliamentary authorities to see whether he can still contribute to the Commons.
I think it is fair to say this has not come at the best time for Mr Johnson: he has big decisions to make on Brexit and what happens when England’s lockdown ends on 2 December.
And it is also worth bearing in mind he was extremely ill with coronavirus earlier in the year and we do not know what getting the virus does for a person’s immunity.
Over the weekend, senior Tory MPs said Mr Cummings’ departure was a chance to “reset government” and a series of announcements are planned for this week, including the government’s 10-point plan for a “green industrial revolution”
A meeting between the PM and the Northern Research Group of backbench Tory MPs had been scheduled for Monday.
And talks over a post-Brexit trade deal with the EU are due to restart in Brussels later.
Meanwhile, in other coronavirus developments:
The UK government announced another 24,962 confirmed Covid cases on Sunday, as well as a further 168 deaths within 28 days of a positive test.