That question requires somewhat more of an answer than the assertion there is a global shortage.“Why haven’t we enough vaccine?”
One of the reasons is insufficient glass suitable for making vials. Another is insufficient fill and finish capacity even were the glass available.
I believe all the glass comes from outside the UK - EU and USA (though there could be other sources).
On 31/12/2020, the UK government claimed:
“We will start a vaccination programme using this vaccine next week, with 530,000 doses available from Monday and tens of millions by April 2021.”
I put it to you that things like vaccine manufacturing should be considered in a similar vein to what the USA call strategic reserves. Maybe we do not need the capacity all the time, but it could be worth subsidising factory builds to ensure that, if needed, they can increase that capacity dramatically.
Similar arguments apply to PPE manufacture.