The original claim regarding the EU dragging its feet over signing the contract was made by the AstraZeneca CEO, not the UK government. And the UK's contract is
not entirely the same as the EU's. For example, the EU waived its right to sue AstraZeneca for delivery failures, something the UK did not. This article by Politico does a good job of going beyond the rather reductive coverage (both pro-UK and pro-EU) in most of the press coverage of this affair, and digging more deeply into the facts:
https://www.politico.eu/article/the-key-differences-between-...
The conclusion, at least as I interpret it, is that both the UK and the EU can reasonably claim to have priority, based on their respective contracts, but that the UK did a better job than the EU in making theirs enforceable. Hence, AstraZeneca has prioritised them, while the EU has been forced to resort to political rather than legal measures to attempt redress (publishing the contract, export controls, etc.). And the UK's closer ties to the AstraZeneca vaccine project likely did mean they started work on the UK supply chain somewhat earlier than in the EU, even although the final contracts were signed essentially simultaneously (one day apart).
I honestly don't really see this as an affair with clear good guys and bad guys, but it seems like most people are determined to do so, and inevitably along the lines of their pre-existing sympathies.