I saw somewhere ( can't remember where as I have read various articles on this recently) that EU countries can order vaccines, but not from the firms who are part of the main EU vaccine contract)
So Hungary have ordered I think it was 2,000,000 of the Sputnik vaccine from Russia.
I suspect (but not certain) that we were able to go it alone as we were leaving. I think the EU asked us to join in rather than put pressure on us to join in as they would if we hade still been a full member. I know Germany and a couple of other countries were thinking of going it alone but then a decision was made (not sure if by the Commission or by the 27 leaders) that there would be one EU contract for every one (with the exception mentioned above)