That is not quite true, it doesn't only target the UK. The export requirements apply to basically everyone except third-world countries through Covax and Switzerland/Norway/Ukraine/Israel due to existing treaties.
But it is true that the AstraZeneca/UK-situation was the trigger event that lead to the public noticing that something was amiss.
There is/was a contract dispute between the EU and AstraZeneca regarding supply of the Oxford-AstraZeneca vaccine. The EU wanted AstraZeneca to supply additional vaccine from it's UK-based factories, which are already contracted to supply the UK.
The export registration requirements (not an export ban) are, at least in part, in response to this dispute.
Well, the contract with the EU included the UK factory(ies) as a (potential?) supplier to the EU.
UK signed the contracts slightly earlier and jump-started the programme by issuing an emergency approval a few weeks earlier than the regular approval by the EMA.
And above all, it seems despite all efforts of coordination and treaties (COVAX), almost all players (except Norway) are playing the auction game and hoarding.
This is a global pandemic and these "selfish" actions will have global effects :(
The rest of the world will get it's vaccines after the first-world states are all vaccinated. And while it sucks to live in a third-world country where vaccinations will come 2022 or 2023 maybe, I can't see any other way, except if the third world would do their own production. Letting more people in the first world die to save some in the third world would be politically impossible.
The problem is that letting the virus continue to circulate unchecked in the developing world just gives it more opportunities to mutate into new, possibly vaccine-resistant variants. Variants can then spread back to infect the first world, and as we've already seen, this can happen quite quickly.
A global vaccination strategy is needed if we really want to get on top of Covid for the long term.
There are two possible strategies for the problem you describe:
Either you vaccinate everyone world-wide at the same time as quickly as possible. Then mutations that make the virus resistant to vaccinations only have the time to occur during the time it takes to vaccinate. However, we do not have sufficient production capacity for doing this. We would have to wait a few years before even starting the vaccinations, otherwise the virus would "mutate away" from the vaccine. Or it would mutate away, if the campaign took too long, because everyone is waiting for the slow drip of doses...
Or you do divide and conquer: Put up travel restrictions, quarantine and testing regimes to split up the problem into smaller areas and subsets of the global population. Quickly vaccinate each of those, so that the virus doesn't have time to mutate away. If possible eradicate the virus in those regions. Then start with the next set of regions and populations, possibly adapting the vaccine to the variants that have occured there. Eradicate the virus there. Then lift the travel restrictions between the regions where the virus has been eradicated. Repeat until done.
Accidentally, the latter one is what we are doing. However, I fear the travel restrictions are too lax to really make it work, because it isn't really planned, just accidential.
There was misunderstanding and arrogance from EU bureaucrats about how business works. They have already tracked back ( Von Der Leyen in EU parliament, Merkel in media ).