Your belief is therefore that Boris would have decided to wait for the EMA. Anything is possible with that eejit, but I think even he would have realised the MHRA were a faster route to approval.
Ah but you are assuming that Boris would still be PM if BREXIT had never happened which is unlikely.
If BREXIT had never happened, David Cameron would have either stayed on as Tory leader and PM until the 2020 election and run again for a third term, or he would have stood down before the 2020 election to make way for a new leader probably George Osborne. The Labour leader of course would very probably been Jeremy Corbyn.
So in the alternate reality, we would have had either PM Cameron, Osborne or Corbyn, and of the three I can only think that Cameron would have vetoed Britain joining the EU vaccine programme.
Of course it's also possible that the 2020 election would have been cancelled because of Covid, in which case we would have either had PM Cameron or Osborne.
The other thing which you are discounting is the pro-EU culture in Whitehall. I'd imagine that the Sir Humphries were very against the UK not taking part in the EU's vaccine scheme, even though we left the EU, as there were accusations of petty nationalism and the like when it was announced that the UK was buying it's own vaccines. So if we'd have never left, especially if we'd voted to stay in the EU in 2016 the pressure for us to take part in the EU's vaccine programme would have been immense and I'd have thought that it would have been deemed unthinkable not to take part.