If the EU contractually agreed to use the UK sites to produce vaccines for the EU on a best efforts basis but they also contractually agreed to prioritise delivery to the UK when they signed with them months earlier (which seems likely to be the case), then I'm not sure how that helps them.

IANAL either, but from including similar wording in numerous contracts on the advice of lawyers, I'm reaosnably sure that committing on a best efforts basis would not require breaking your other contractual obligations.