It sounds like AZ are in an interesting position. If the media i've read is correct (my usual Tory sources), AZ signed a contract with the UK to deliver 100m doses of the vaccine made in UK factories. That contract also says that those factories can't supply any other country until we've had all our 100m doses.
The EU has signed a best endeavours contract that says that supplies will come from a 4 factories, 2 of which are in the UK. Their agreement was agreed 3 months later than the UK deal. I would expect that legally, the UK deal supersedes the EU deal, so the EU contractually aren't entitled to have any vaccine from UK factories until the UK contract has been fulfilled.
Which leaves the EU in a position where they need to attempt to bully AZ with blackmail about future access to the EU market in order to try to twist AZ's arm into breaking the contract that have with the UK.
All in all, it appears to me that the EU have royally f*cked this one up and our much derided government has done even better than we thought.
Interestingly, Oxford was about sign a deal with Merck to develop the vaccine until our government stepped in and funded the vaccine's development. Merck have just announced they've abandoned their own efforts to create a vaccine due to 'disappointing results from the prototype'.