My understanding of the issue (happy to be corrected) is that the UK signed a deal with AstraZeneca that included all doses being manufactured in the UK plant supplying the UK its doses before they ship any doses from the UK internationally to fulfill later agreed international orders. That's what they're doing. Once the UK has received what it purchased, long before the EU, then doses will be shipped out of the UK.
The EU signed a deal months later. Their initial doses are manufactured in Europe. There's production issues in the EU and they won't get as many doses right now as they expected. All because they waited 3 more months to order. As a result of that 3 month delay they've had less time to get the European production plant scaled up. So they think they should receive doses manufactured in the UK which the UK has already purchased exclusively 3 months earlier.
To try and achieve this they are threatening to impose export restrictions to the stop the UK from receiving deliveries of the Pfizer vaccine that is manufactured in the EU despite the UK having purchased them already, and again, purchased them before the EU.
The EU are in a mess of their own making.