Unlike the EU the UK and the US imposed export bans on vaccine and the UK very probably had a shady deal going with Astra-Zeneca to deliver more to them than the EU. The criticism of the european vaccination efforts is always a bit schizophrenic in so much as it praises the anglo-american success but cries havoc when the EU just stops one single shipment from being exported while not mentioning the export bans in the UK or US at all.
Add to that that american and british medical authorities were laxer in their admission of the vaccines while the EMA exercised due diligence. In the usual patterns of Brussels-bashing the EMA would certainly have been criticised for sloppiness had they acted like the british or american authorities.