Care homes have said Matt Hancock's promise of nationwide testing to allow visits by Christmas is unlikely to be achieved without urgent funding, adding that it is "distressing and risky to raise expectations without the policies in place to achieve this".
"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", he added, saying he would lead the virus response from his Downing Street home.
In a video message posted on Twitter, he said he was "as fit as a butcher's dog" with "no symptoms" after meeting Mr Anderson, and that he is "bursting with antibodies".
Johnson, who contracted the virus in April and spent three days in intensive care as his symptoms worsened, met with a small group of lawmakers for about a half-hour on Thursday, including one, Lee Anderson, who subsequently developed symptoms and tested positive.
The Health Secretary committed to a major expansion of visitor testing over the next two months as pilots in 20 care homes across Hampshire, Devon and Cornwall began on Monday.
Four other Conservative MPs who were at the meeting last week - Katherine Fletcher (South Ribble), Andy Carter (Warrington South), Lia Nici (Great Grimsby) and Brendan Clarke-Smith (Bassetlaw) - are also self-isolating.
Johnson has repeatedly spoken about how the apparent brush with death this year changed his outlook.
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His comments were echoed by the Prime Minister's spokesman, who told reporters: "We need to assess how the pilots go but this is clearly a really hard issue and where we can do more to allow people to spend time with their loved ones then that is obviously something we want to do".
"We don't propose, and allow vaccines in this country, unless they pass some of the most stringent safety requirements in the world", he said.
'We are seeing very little effect from Tier 1 and I think when we look at what tiers may be there in future we will have to think about strengthening them in order to get us through the winter months until the vaccine is available for everyone'.
"So it's a really important step", he added.
However, Johnson addressed all his Downing Street staff via Zoom, and reiterated his commitment to "two absolute Government priorities", according to his spokesman.
His confinement comes as negotiations with the European Union over Brexit enter a decisive final sprint, with critical announcements being trailed - ahead of Johnson's isolation - by Downing Street to tackle the virus.
The quarantine requirement comes as Johnson and the United Kingdom begins discussions over a post-Brexit trade deal with the European Union.