Mr Johnson said the fact he was “bursting with antibodies” having had coronavirus before would not impact on his having to self-isolate after his meeting with Tory MP Lee Anderson.
It comes as Mr Johnson’s bid to reframe his tenure as Prime Minister following a fallout among his advisers, resulting in Dominic Cummings and Lee Cain leaving 10 Downing Street, has been left in limbo.
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The Prime Minister, who was admitted to intensive care with coronavirus in April, said he was notified by NHS Test and Trace on Sunday he must self-isolate and will now remain at Number 10 for a period of 14 days.
In a video message he tweeted he was “in good health” and that has no symptoms.
He said: “Hi folks, 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 – so many people do in my circumstances.
“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.”
Mr Johnson said he was self-isolating with a “high heart” the country was getting on top of the virus, with rapid speed testing and hopes of having a vaccine roll-out before Christmas providing reasons for encouragement.
Questions have been raised about a photo taken of the PM and Mr Anderson, showing the men closer that two metres apart.
Health Secretary Matt Hancock was asked whether more care should be taken when dealing with someone as important as the Prime Minister and said they were “very careful” and met frequently via Zoom.
He also told Times Radio: “I think the important thing is that everybody has to follow these rules and the Prime Minister is no exception.”