The fact that the EU and UK are already fighting illustrates how imporant the EU is. Imagine if the EU didn't intervene in the vaccine programme and it was 28 rich countries trying argue to 28 contracts with AZ instead of just two -- and all the complexity that emerged from just two contracts.
The EU is fighting with Astrazenica. The UK has mostly kept out of it - only just commenting once the EU decided to change export rules and around the Northern Ireland agreement.