You are correct - the vaccine will still work so long as the one spike protein the vaccine targets does not change.
The US has a different strain now - over 99% of cases for the last several months have been a new, more contagious virus. The mutation causing the increase in contagion was on a spike protein, but not the one targeted by the vaccine. So the vaccine still works against the dominant strain.
As for the newest strain from the UK, it is likely already here. They have no idea if the vaccine is effective against the newest strain. They are still trying to figure that out. Both Pfizer and Moderna are testing right now against the new, 17 mutation mutant . . .