A delay in deliveries from India and the need to retest a batch of 1.7 million doses is behind the issues with vaccine supply in April.
The problem with a shipment from the Serum Institute of India (SII) has been blamed by the body’s chief on the country’s government, although Mr Johnson said Narendra Modi’s administration has not stopped any exports.
Mr Johnson said: “We have always said that in a vaccination programme of this pace and this scale, some interruptions in supply are inevitable.
“It is true that in the short term we are receiving fewer vaccines than we had planned for a week ago, that is because of a delay in a shipment from the Serum Institute – who are doing a herculean job in producing vaccines in such large quantities – and because of a batch that we currently have in the UK that needs to be retested as part of our rigorous safety programme.
“As a result, we will receive slightly fewer vaccines in April than in March but that is still more than we received in February and the supply we do have will still enable us to hit the targets we have set.”
The over-50s and the clinically vulnerable will still be offered a first dose by April 15, and second doses will be available to around 12 million people in April.
Every adult will be offered a first dose by the end of July, as planned, he said.
“Our progress along the road to freedom continues unchecked, we remain on track to reclaim the things we love, to see our families and friends again, to return to our local pubs, our gyms and sports facilities and, of course, our shops,” he said.
SII chief executive Adar Poonawalla told The Telegraph the delay to a shipment of millions of doses was “solely dependent on India and it has nothing to do with the SII”.
“It is to do with the Indian government allowing more doses to the UK,” he said.
But Mr Johnson told a Downing Street press conference “the Indian government has not stopped any export” but “there is a delay… as there is very frequently in vaccine rollout programmes”.
“It’s very important to stress whatever you may hear about the pressures that different countries are under to deliver vaccines for their public, these vaccines are a multinational effort, they are produced as the result of international co-operation and I want to stress that we in the UK will continue to view it in that spirit.
“We don’t have any bans on exporting stuff and we will continue to co-operate with our European friends.”
The issues with supply came as regulators in the UK and Europe reaffirmed the safety of the Oxford AstraZeneca jab – a vaccine Mr Johnson will receive on Friday.
The Prime Minister said: “The Oxford jab is safe and the Pfizer jab is safe. The thing that isn’t safe is catching Covid, which is why it is so important that we all get our jabs as soon as our turn comes.”