The UK had a head start (due to earlier approval of the AZ vaccine, they were the second ones after the Russins and before the US), of one and a half months or so. The UK gotlucky that AZs prodution in the UK went smoother than the one in Belgium. And cirumstances are in favour of the UK, initial deliviery volumes are low accross the board, regardless of supplier, and a smaller population allows higher per capita numbers in these cases.
The main reason so, IMHO, is the UKs approach and management of the campaign. With NHS, theUK coud build upon one entitiy to run things, the UK streched the second shot and didn't hold inventory back for it. And the UK seems to have proper operational supply chain management in place.
The EU (meaning individual member states) on the other hand has a larger population, at least 27 individual entities (Germany adds 16 individual states to that), o central planning (Germany has none on the federal level and I haven't seen any on state level so far neither), no coherent strategy. Appointment managment doesn't work. The EU also screwed up supply by ordering more in january (volumes that weren't needed) which resulted in further delays. And the list goes on.
In a nut shell, the UK didnt screw with the suppliers supply chains up to end f production and has a grip on the down stream supply chain up to peoples arms. The EU screwed with suppliers and has zero plan about everything after doses are delivered to a national distribution hub.
EDIT: The EU has to coordinate 27 nations and has to avoid an EU-internal bidding war. The UK doesn't.