Mr Johnson faces growing unease from within his own party over the lockdown, which will begin on Thursday and last until December 2.
The Prime Minister has sought to win them over with warnings about a high death toll if the situation continues.
Mr Johnson told the Cabinet that the R number – the reproduction rate of the virus – was “only just above 1” and the lockdown would bring it back below that threshold.
He acknowledged that “we don’t want to be doing things to repress liberty, we don’t want to do anything to damage our economy” but “we would see fatalities running in the thousands if nothing was done”.
However, the rapid tests could be “possibly decisive” in defeating the virus and there were also better drugs and the prospect of a vaccine.
“Amid the uncertain gloom of November, I see light ahead and I’m absolutely certain that we will have better days before us,” he told ministers.
“Let’s all work flat-out as a Government to repay the confidence of the people who are doing the right thing and following the latest autumn measures.”
Mr Johnson’s efforts to win public support were not helped by two Cabinet ministers appearing confused over the restrictions which will come in on Thursday.
Communities Secretary Robert Jenrick suggested that an entire household could meet up with a friend, before then contradicting himself.
And Chancellor of the Duchy of Lancaster Michael Gove apologised after incorrectly indicating that people could play a round of golf or game of tennis with a friend.
The official guidance states that people in England can exercise or visit outdoor public places either with their household or one person from another household – although children under school-age with a parent will not count towards the limit on two people meeting outside.
On BBC Breakfast, Mr Jenrick was asked if a family could go for a walk with a friend.
The minister answered: “Yes.”
However, when presenter Louise Minchin pressed him, asking whether this applied to four people and one person, Mr Jenrick said: “Yes, so you can go out in your own household, or with one other person.”
Mr Gove admitted his mistake after wrongly suggesting during a question and answer session with constituents that people would be able to play singles tennis or golf in pairs during the impending lockdown.
On Tuesday morning, Mr Gove said: “My apologies, I got this wrong.
“Outdoor leisure facilities including tennis courts and golf courses will be closed from Thursday.”
England’s lockdown will end on December 2, with the Government hoping to reintroduce a localised tiered system of restrictions.
Mr Johnson hopes that a mass testing campaign, using equipment which can deliver a result in a matter of minutes, could be a route out of the coronavirus crisis.
The pilot scheme in Liverpool will see half a million people offered regular testing from Friday, with 2,000 military personnel helping with the logistics.
If the pilot is a success, millions of the tests could be distributed by Christmas, Mr Johnson said.