Boris Johnson, six Tory MPs and two political aides are self-isolating after a breakfast meeting inside Downing Street last Thursday.
One of the MPs, Lee Anderson, later tested positive for Covid-19, and on Sunday the prime minister was told to self-isolate by NHS Test and Trace.
In a video from No 10, Mr Johnson urged others to "follow the rules" if contacted by the system.
The PM's official spokesman insisted that Downing Street is "Covid-secure".
He said "social distancing did happen" but factors such as the length of the meeting were considered by Test and Trace.
Mr Johnson, who was admitted to intensive care with coronavirus seven months ago, spent about 35 minutes with Mr Anderson - who lost his sense of taste the day after the meeting.
The five other MPs self-isolating following the meeting with "Red Wall" Tories include:
- Heywood & Middleton MP Chris Clarkson
- South Ribble MP Katherine Fletcher
- Warrington South MP Andy Carter
- Great Grimsby MP Lia Nici
- Bassetlaw MP Brendan Clarke-Smith
Mr Johnson's spokesman declined to name the aides but suggested they were not Lee Cain or Dominic Cummings, who left Downing Street last week.
Jacob Young, MP for Redcar, is also self-isolating - but said he was not at the meeting - while Basingstoke MP Maria Miller has said she is self-isolating after having been contacted by Test and Trace.
Labour leader Sir Keir Starmer said the prime minister was right to self-isolate as "it is important for all of us to say that we have got to comply with the advice and guidance".
Hi folks, I’ve been instructed by our NHS Test & Trace scheme to self-isolate for two weeks, after being in contact with someone with Covid-19.— Boris Johnson (@BorisJohnson) November 16, 2020
I’m in good health and have no symptoms, and will continue to lead on our response to the virus & our plans to #BuildBackBetter pic.twitter.com/yNgIme8lOz
The PM's period of isolation began 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".
The prime minister had been expected to lead a No 10 news conference on Monday but Health Secretary Matt Hancock took his place.
However, Mr Johnson is hoping to take part in Wednesday's Prime Minister's Questions session in the House of Commons virtually, Downing Street said.
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."
Photos of Mr Johnson and several Tory MPs show them standing close together. The prime minister had to self-isolate after one of them, Mr Anderson, developed Covid symptoms.
Guidelines for offices require social distancing of 2m (6ft), or 1m plus precautions such as frequent cleaning and one-way systems where that is not possible.
No 10 is yet to respond to a request from BBC Reality Check for details of the Covid-secure guidelines in Downing Street.
But the PM's spokesman said "social distancing did happen" and that the picture shows Mr Johnson and Mr Anderson "stood side-by-side, rather than face-to-face".
However, Test and Trace guidance defines a close contact as someone you spent more than 15 minutes with at a distance of under 2m. Mr Johnson's meeting with Mr Anderson lasted about 35 minutes and he would therefore be required to self-isolate if they were not more than 2m apart.
In his video posted on Twitter, the PM said: "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."
According to No 10, the prime minister has had at least one antibody test for coronavirus.
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."
What is self-isolation?
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 for the virus, and he would be working from No 10.
The new policy plans follow the dramatic departure of the PM's chief adviser Dominic Cummings last week.
Over the weekend, senior Tory MPs said his exit 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 is scheduled to take place via online video conference later on Monday.
And talks over a post-Brexit trade deal with the EU have resumed in Brussels.
Meanwhile, in other coronavirus developments:
- Two new "mega labs" will open early next year to try to double the UK's daily coronavirus testing capacity, the government has said
- A major trial of a vaccine to protect against Covid-19 has launched in the UK - the third such trial in the country
- The Supreme Court will hear a hotly-contested case about insurance payouts for small businesses who were unable to trade owing to lockdown later
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.