Health officials said volumes for first doses of the jab will be "significantly constrained' from the end of March, with the shortages reportedly due to issues with doses being imported from India.
More than 25 million people in the UK have now received a first dose of a coronavirus vaccine, but the NHS has warned of a month-long “significant reduction” in weekly supply of the jabs.
One expert warned that the "ripple effect" of shortages could last for months.
But on Thursday, Cabinet minister Robert Jenrick said while the vaccine rollout would be slightly slower than the government had hoped, there was “no reason to believe” its roadmap would be delayed.
The housing secretary told Sky News: "There’s no reason to believe the roadmap is affected by this temporary shortage in supply. There’s no concern that we are off course on the roadmap."
He said there was every reason to believe that supplies would increase in May, June and July, and said "nobody who has an appointment should be concerned".
He added: "We do think there are going to be some supply issues in the weeks ahead but this isn’t anything that people should be worried about, we’re still on course to meet our targets.
"Nobody who has an appointment should be concerned, you’re still going to get your second vaccine, all those appointments will be honoured.
"But we always said right from the beginning that a new manufacturing process would have its lumps and bumps, that has been the case in the past and I’m sure it will be in the future."
Watch: Pfizer and AstraZeneca deny domestic coronavirus vaccine shortage
The concerns come as the European Medicines Agency (EMA) was due to meet on Thursday to discuss the Oxford/AstraZeneca vaccine after a dozen European countries suspended rollout of the jab over isolated cases of blood clotting.
In England, concerns over shortages arose after a letter to local health leaders asked vaccination centres and community pharmacy-led services to close unfilled bookings and “ensure no further appointments are uploaded” to booking systems in April.
NHS bosses said that as a result of the supply issues, people under the age of 50 should only get the jab if they are in a priority group, meaning younger adults could face a longer wait to be be vaccinated.
Dr Simon Clarke, associate professor in cellular microbiology at the University of Reading, said the shortages would "undoubtedly" make meeting target dates lifting restrictions more difficult.
He said: "By pushing back the under-50s first doses, their second doses are also being pushed back. If full vaccination becomes required for holidays abroad or even more mundane things like going to the cinema, millions of younger people may end up being excluded from participating for the whole summer."
Health secretary Matt Hancock told a Downing Street press conference on Wednesday that vaccine supply was "always lumpy" and insisted the UK was on track to meet the target of offering a first dose to all over-50s by 15 April.
But Labour has urged the government explain what the supply issues are and how it is aiming to resolve them.
A Pfizer spokeswoman said deliveries "remain on track" for the first quarter of its 40 million dose agreement with the UK, with a “steady supply of vaccines” delivered to the nation.
Meanwhile, an AstraZeneca spokeswoman said: "Our UK domestic supply chain is not experiencing any disruption and there is no impact on our delivery schedule."
Watch: How England will leave lockdown