I have an uncle who works at BA and he has got me upgraded before, only to World Traveller Plus though. I've also been upgraded at check in (a sort of apology/minor compensation for a late running flight causing a missed connection in London), again to WTP. There were a couple free seats in Club World on both occasions so I'm guessing that BA only permit 1 class upgrade (ignoring ICAO rules on cabin classes).
When my uncle got me upgraded, he wrote a letter to the CSD for the flight and it was handed to her with the other paperwork for the flight. When the flight was fully boarded and the doors shut one of the crew came to find me and moved me. Just after take off the CSD came over to me, introduced herself and wished me a pleasant flight.
Best of luck for your upgrade and fingers crossed for that upper deck upgrade!