"We've got Brexit to thank for our success in the vaccine situation. "
Britain has handled the situation much better than the EU, but I don't think that is because of Brexit specifically.
It may be that the UK was acting more in an "independent spirit" and felt it had something to prove, but the vaccine task force for example was helped along by yhr fact that the UK has an advanced scientific and epidemiological base. In fact that was as I recall the reason many said the UK would be better able to cope with a pandemic : in fact that turned out not to be the case, as there were other more significant factors.
Brexit, what with handling of how to do it, the arguments over it, the wrangling and the initial post-Brexit situation, has been a disaster so far, from day one post-referendum onward. but it is too early to say whether it will remain that way.