The prime minister said "people have just got to understand" that taking a step out of lockdown will result in more infections, adding: "Sadly we will see more hospitalisation and deaths."
It came after government expert Professor Jeremy Brown said there could be up to 50,000 deaths, despite Covid-19 vaccines, if a third wave of the virus rips through the country.
But Mr Johnson said he "can't see any reason for us to change the road map, to deviate from the targets that we have set ourselves".
Under his roadmap, England will take its next step out of lockdown on May 17, before a final reopening on June 21, which will even allow nightclubs to open.
To achieve those goals the PM urged everyone to remain cautious, especially amid the reopening of hospitality venues with outdoor services, hairdressers and non-essential shops.
Deaths will 'inevitably' rise, says Boris Johnson:
"If we are to get there in the way that we all want, people continue to be cautious and they continue to exercise restraint and just do the basic things to stop the spread of the virus - washing your hands, giving people plenty of space, doing things in fresh air," he said.
Professor Brown, a member of the Joint Committee of Vaccination and Immunisation, warned that, even with the vaccination programme in place, there could be a “big third wave” of Covid-19, with potentially tens of thousands of deaths.
“I feel mighty relieved that we are now in a position where a very high proportion of the vulnerable population have been vaccinated so, if control of the virus is lost, then the damage it can do will be relatively restricted,” he told BBC Radio 4’s Today programme.
“But when I say relatively restricted, what I mean is that a big third wave could still end up with 30,000 to 50,000 deaths, potentially, if it was a similar sort of size to the previous waves that we’ve had."
Mr Johnson encouraged people to get coronavirus vaccines when offered, insisting he was "very confident" about vaccine supply.
England is now inoculating over-45s following the success in offering all over-50s their first dose.
The PM told reporters in Downing Street: "This always was going to be the 'second dose' month and people should come forward for their second doses and people who are called from the 45-49 (age) group should come forward and get theirs."
He warned that although the numbers of infections, hospital admissions and deaths are down, the reduction "has not been achieved by the vaccination programme" but rather the lockdown.
"Of course, the vaccination programme has helped, but the bulk of the work in reducing the disease has been done by the lockdown," he said.
Prof Brown said that "although the vaccines are important, there are the components to controlling this virus that are important and that is the social distancing measures that we have".
“Now, those will be less necessary the higher proportion of the population gets vaccinated, which is another reason why young people vaccination is important, is that for population control, the bigger the proportion of the population that the vaccinated, the less we will need in a way of social distancing.”
He added that young people would also want to get their jab to reduce chances of getting long Covid and reduce their risk of infecting others.
The government has now begun phase two of the vaccination programme, which targets adults aged 40-49.
The next group after over-40s will be adults aged 30-39, and then all adults aged 18-29.
The government has pledged that all UK adults will be offered their first dose by the end of July.
"It's great that we have managed to achieve the target of getting everyone in the one to nine (priority) groups vaccinated by the deadline, by the timetable - a little bit ahead actually, 32 million people now have got their first dose, which is terrific," the prime minister said.
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