"This is a very perilous moment because everybody can sense that the vaccine is coming in and they can see that the UK is vaccinating large numbers of those that need it most," he said on Monday during a visit to a vaccination center in Bristol, located in southwest England, about 193 km west of London, Xinhua news agency reported.
"My worry is...that this is the moment when that degree of false confidence, false complacency, and that when you look at what has happened in the NHS (National Health Service) that complacency is not merited," he said.
According to the prime minister, 2.4 million coronavirus jabs have been administered across Britain.
Seven new mass vaccination sites in England opened Monday, as the country races against time to bring the pandemic under control.
Earlier Monday, Chief Medical Officer for England Chris Whitty warned that the "most dangerous time" of the coronavirus pandemic in Britain has yet to come before vaccine rollout has an impact.
The next few weeks will be "the worst" of the pandemic for the NHS, he told the BBC, urging the public to minimize all unnecessary contact with others.
Johnson and Whitty made the warnings after Britain surpassed the grim milestones of 3,000,000 Covid-19 cases and 80,000 coronavirus-related deaths on Saturday.