Not sure I understand your second sentence, it might be saying what I am about to write. From reading several articles on the issue, the EU seems to demand that the slow-down in production be shared equally across orders. This puts AZ in a pickle: it would then mean they are not only breach of contract with the EU but also UK. Hence, they publicly reiterate the "first come first serve" argument which resonates well in the UK media and rallies support (I think AZ is pitting EU against UK in all of this). I do not believe the "first come first serve" principle is how supply chains like this usually work though. Totally not my field of expertise, but hearsay from some friends working in supply chain management.
It's not actually a "first come first serve" argument as I understand it - it's that contractually the UK and EU supply chains are separate, each contract only requires them to supply the contracted vaccines from that supply chain, and the EU one is in much worse shape yields-wise because the EU dragged their feet on signing the contract for internal political reasons leaving AZ with less time to fix the problems. (There's a contractual provision in the EU contract allowing them to supply some vaccines from the UK which the EU is trying to stretch into them requiring it.) The whole claim that AZ is doing first come, first serve and it isn't fair seems to be EU spin, and pitting the EU against the UK seems to be an intentional EU tactic. In particular, as I recall EU officials started making evidence-free claims early on that AZ had been exporting doses from their European facilities to the UK and this caused the shortage, something they deny and that no evidence has been found for despite raids on their facilities.
> As soon as we have reached a sufficient number of vaccinations in the UK, we will be able to use that site to help Europe as well. But the contract with the UK was signed first and the UK, of course, said “you supply us first”, and this is fair enough. [1]
It’s just an out of context quote and the problem is more complex than this, but I think it’s fair to say that you could interpret this statement as “first come first serve” and since the contents of the contract with the UK are still unknown, this also raises some questions.