He confirmed Tuesday's cabinet meeting will also go ahead mostly by video conference, with ministers dialling in instead of piling round a cramped table as part of social distancing measures.
Downing Street also confirmed the UK's top civil servant in the EU trade negotiations, David Frost, is self-isolating after showing COVID-19 symptoms.
But Number 10 reiterated the plan is still for talks to conclude by the end of the year, despite Brussels' chief negotiator Michel Barnier also being in self-isolation after testing positive for the virus.
Meanwhile, Mr Johnson's spokesman has signalled that self-employed people would get more help, after being left out of the original round of financial measures to support businesses.
"We appreciate the difficulty they are in and officials are working round the clock," he told journalists at a briefing on Monday.
Charities were also assured ministers were working on measures to help the third sector.
And after speculation the Olympics due to take place this summer in Japan could be delayed, the UK's sports minister called for the international organising committee to make a definitive decision soon and consider postponing the games.
It comes as the government prepares to rush through emergency legislation to tackle the coronavirus outbreak, hoping to pass a new law through the Commons on Monday.
Health Secretary Matt Hancock told Sky News' Kay [email protected] a decision on whether to further lockdown the country to stop people flouting social distancing rules would be taken "very soon".
"We will enforce and bring in further strong measures if we need to - but I'd much rather people follow the rules themselves, it would be much more straight forward," he said.
"If we need to go further in terms of people's interactions then we will."