He said he still has a "mild" coronavirus symptom, a temperature, and in accordance with advice, he must continue his self-isolation.
In the video, he appealed to "everybody thinking about this weekend, and what may be some fine weather" and warned them "please, please stick with the guidance now".
"I reckon a lot of people will be starting to think that this is all going on for quite a long time and would rather be getting out there, particularly if you’ve got kids in the household, everybody may be getting a bit stir crazy, and there may be just a temptation to get out there, hang out and start to break the regulations," he said.
“I just urge you not to do that."
He added: “This country has made a huge effort, a huge sacrifice, done absolutely brilliantly well in delaying the spread of the virus.
“Let’s stick with it now – remember that incredible clapping again last night for our fantastic NHS. We’re doing it to protect them and to save lives.”
On his condition, he said he is “feeling better" after seven days of isolation, but "must continue my self-isolation" until his high temperature goes.
He announced on Twitter last Friday he had tested positive for coronavirus and had symptoms including a cough and fever.
He fell ill around the same time as Matt Hancock, however the Health Secretary has now returned to work following seven days isolation.
Mr Hancock said he was unable to eat, drink or sleep properly for "two days or so" owing to the impact Covid-19 had on him.
Describing his own experience as "pretty nasty", he told Good Morning Britain: "I had two days or so when it was like just razors in your throat, a very, very sore throat. I couldn't eat and I couldn't drink.
"The worst bit was on the way down, worrying how bad it would get because we've all seen how bad it can get and it seems to be indiscriminate."
In his message from his flat in 11 Downing Street, the prime minister reiterated that message.
“We’re working clearly the whole time on our programme to defeat the virus. You’ll have seen the big announcement yesterday about 100,000 tests a day by the end of the month.”
Downing Street has confirmed that the target of carrying out 100,000 coronavirus tests a day applied to the whole of the UK – and not just England.