On BA flights, I have been offered cash upgrades from Y to Y+ as well as Y to J (on the same flights) in the LHR lounges and at check-in in other countries.
I was going to say, but couldn't be sure and didn't want to offer disinformation, that the rules on only allowing a single cabin upgrade are probably a bit more relaxed at the airport when selling upgrades for cash. However, I believe it's only a single cabin when BA offers its upgrades for sale online in advance of the flight.