The EU signed contract with AstraZeneca 1 day before the UK did, claims https://twitter.com/DaveKeating/status/1372897637469458432
There's no export restriction, it's more subtle.
UK has funded Oxford vaccine development on condition that UK gets preference for doses produced in UK (if not elsewhere too).
This has exactly the same practical effect as an export ban, but it technically isn't an export ban, hence the recent grandstanding from UK politicians.