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.
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".
Health Secretary Matt Hancock will hold a No 10 news conference later, which the prime minister had been expected to lead.
But 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."
Asked about photos of the prime minister and individual MPs taken at the meeting, Downing Street said they were standing side by side.
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