The issue with the EMA approval date is a red herring, in my opinion. Unfortunately it gets given a lot of attention (especially in the UK press) even by organisations that should know better.
The most important thing to remember is that both the UK and EU pre-paid for AZ to manufacture their vaccine pre-approval. The date of regulatory approval and the manufacturing schedule are supposed to be completely decoupled.
It's true that the UK got their vaccine order in first and nobody is denying that. That's why the UK was getting shipments from AZ back in December. When the EU finally signed their contract they were told that their deliveries could start in February.
While I doubt the EMA is going to comment publicly on the timing of their decisions, I don't think it's a coincidence that their approval of AZ was done in late January. They already knew that the meaningful supplies were starting in February so they simply collected as much data as they could before making the "go/no-go" decision.
So while the "feckless EU bureaucrats screwed it up" storyline is forever popular (both in the UK and EU press) they seem pretty blameless on the issue of AZ approval. They just had to get it approved before the manufacturer was ready to start deliveries and they managed that.
What kicked this into a crisis is that AZ announced that their February deliveries to the EU would be less than half of the expected amount. The EU's position is that the UK and EU should be treated equivalently at this point: they both pre-paid for certain quantities to be delivered in February, so any production shortfall should be shared. Needless to say, the UK sees it differently and doesn't want any UK-based manufacturing to go to the EU. Hence we got this ugly diplomatic standoff.