A new letter from NHS England sent to local vaccination sites across the country says volumes for first doses are going to be "significantly constrained".
This disruption could last for a whole month, with the government's vaccines taskforce explaining this is linked to "reductions in national inbound vaccines supply".
A statement says: “The government’s Vaccines Taskforce have now notified us that there will be a significant reduction in weekly supply available from manufacturers beginning in the week commencing March 29, meaning volumes for first doses will be significantly constrained.
“They now currently predict this will continue for a four-week period, as a result of reductions in national inbound vaccines supply.”
Now vaccination centres are being told to close unfilled bookings from March 29 onwards and ensure no appointments are given for the month of April.
The disruption to supply is expected to have a knock-on effect in Scotland.
At Wednesday’s Downing Street press conference, health secretary Matt Hancock insisted it was simply a “standard” technical letter.
He said: “Vaccine supply is always lumpy and we regularly send out technical letters to the NHS to explain the ups and downs of the supply of the future weeks and what you are referring to is a standard one of those letters.”
Mr Hancock also told the conference “we fully expect” vaccine contracts to be delivered on after European Commission president Ursula von der Leyen suggested the EU could block exports.
The health secretary said: “The Oxford-AstraZeneca vaccine was produced from research funded by the UK Government, tens of millions of pounds.
"We set up the supply chain, not just here in the UK, but we helped set up the supply chain in the EU.
“This vaccine is provided at cost to the whole world and we legally signed a contract for delivery of the first 100 million doses for people here, for people in the UK.
“So, the supply of vaccines from EU production facilities to the UK is indeed fulfilling contractual responsibilities.”
It was earlier announced almost half of British adults had received their first dose of a coronavirus vaccine.
The Department of Health said 25 million people had received the first dose.