Boris Johnson has warned that the reduction in coronavirus infections, hospitalisations and deaths "has not been achieved" by the rollout of COVID vaccines.
The prime minister, speaking the day after the latest easing of lockdown restrictions, instead said it was the national shutdown that had been "overwhelmingly important" in driving down COVID rates.
Nearly 40 million vaccine doses have now been given across the UK, with those aged between 45 to 49 now able to book their jab appointments.
They are being invited for vaccines after the government’s target for offering a first dose to priority groups one to nine – including all over-50s – was reached three days early.
But, speaking in 10 Downing Street, Mr Johnson suggested the millions of vaccines given over the past few months were not key to the reduction in COVID levels.
He said: "The numbers are down – of infections and hospitalisations and deaths.
"But it is very, very important for everybody to understand that the reduction in these numbers – in hospitalisations and in deaths and infections – has not been achieved by the vaccination programme.
"People don’t, I think, appreciate that it’s the lockdown that has been overwhelmingly important in delivering this improvement in the pandemic and in the figures that we’re seeing.
"And so, yes of course the vaccination programme has helped, but the bulk of the work in reducing the disease has been done by the lockdown.
"So, as we unlock, the result will inevitably be that we will see more infection, sadly we will see more hospitalisation and deaths, and people have just got to understand that."
However, the prime minister added that "at the moment" he couldn’t see "any reason" to change his roadmap for easing lockdown restrictions.
The next stage of the roadmap, on 17 May, will allow restaurants and pubs to resume indoor service and see most rules on gathering outdoors lifted.
Mr Johnson also plans to remove all legal limits on social contact on 21 June.
"It is very, very important that if we’re to get there in the way that we all want that people continue to be cautious and they continue to exercise restraint and just do the basic things to stop the spread of the virus," he added.
"So, you know, washing your hands, giving people plenty of space, doing things in fresh out as much as you can."
Pharmaceutical company Johnson and Johnson (J&J) is delaying the rollout of its "one-shot" vaccine in Europe, which has yet to be approved in the UK, after the US halted its own programme after a handful of people developed blood clots.
The clots have been found in combination with low platelet levels in women aged 18 to 48, with symptoms developing six to 13 days after vaccination.
Dr Peter Marks, director of the US Food and Drug Administration (FDA), said treating these clots as normal "may be dangerous" and said the FDA would revise the fact sheet for administering the vaccine.
He said they believe the "probable cause" of the immune platelet response is similar to what is going on with other vector vaccines – such as AstraZeneca’s – and occurs "very, very rarely".
US chief medical adviser Anthony Fauci said authorities are investigating the cases "to understand the mechanisms… shed some light".
He added: "This is a really rare event, there have been six out of the 6.85 million doses, which is less than one in a million."
There has been a warning of a significant reduction in the UK’s weekly vaccine supplies this month but the Department of Health and Social Care insisted the J&J delay would not hold up the rollout.
Ministers have previously pointed to delays in the supply of five million doses of the Oxford-AstraZeneca vaccine from India, as well as a need to retest a batch of 1.7 million vaccine doses.
But the prime minister said he was "very confident about our vaccine supplies" as the government aims to offer all UK adults a first dose by the end of July.
"This was always going to be the second dose month and people should come forward for their second doses," Mr Johnson added, as he reiterated the government’s current focus on delivering second doses to those who have already had one jab.
"And the people who are called (for their first dose) in the 45 to 49 group should come forward and get theirs."
Analysis: A prime minister pushed and pulled
By Jon Craig, chief political correspondent
Boris Johnson’s claim that it’s not vaccinations that have cut COVID numbers but lockdown measures will infuriate anti-lockdown Tory MPs.
These MPs, members of the 70-strong COVID Recovery Group, are already demanding a speeding up of the roadmap out of the lockdown in England.
But in the week of step two of his roadmap, with outdoor drinking and non-essential retail re-opening, the prime minister is being pulled both ways.
While Tory MPs are impatient for the lockdown to end and are furious at new rules on the way, like vaccine passports, scientists are pulling the PM the other way.
You could almost hear the voices of Professor Chris Whitty, Professor Jonathan Van-Tam and Sir Patrick Vallance as Mr Johnson spelled out his cautious message.
He said there would be more infections, hospitalisation and deaths as between now and step four, which is due on 21 June, and people had to understand that.
Shortly before his "lockdown works" salvo, the PM will have been briefed on the south London surge in the South African variant by the Whitty/JVT/Vallance trio.
So it seems the days of vaccine euphoria in Whitehall are over and the SA variant could even slow down the easing of lockdown rules, infuriating Tory MPs once again.