In the US at least, the first doses will go to healthcare providers and ling term care elderly home occupants. They have to get two shots at about one month apart. Chances are the vaccine won't be rolled out to the general public until at least April/May.
There's still much resistance against the vaccine--the traditional antivaxxers, the progressives who are suspicious of the Trump Administration rolling this out so fast, and ethnic minorities who don't trust government-administered medicines at all.
Don't know if the UK is planning a similar schedule, but in the US, May would be overly ambitious to re-open Bway.