At this time, your vaccination status does not change anything for visits to the US from countries subject to the travel ban, so the answer to you original question still stands.
Unless you qualify for one of the limited exemptions to the ban (which I suppose you didn't before, and nothing changed in that respect), your only option is to spend 14 days outside the UK and outside the Schengen Area (or any of the the other banned countries), and of course not transit by any of the banned countries on your way to the US.
Your most likely way to achieve this is probably to spend 14 days in Mexico or some other Central American country, I would think. It will soon be possible via Canada as well (if things go to plan).
NB: do not even consider for a minute trying to spend only a few hours or days in Mexico before travelling to the US. That will not end well.
There's talk about opening up travel to the US for fully vaccinated people, but for now, nothing has happened, and there's no date for that. Might happened tomorrow, might happen in a month, might happen in a year. Or maybe even later.