What is the route you are flying?
There are 3 class (J,W & Y) 777's and there are routes where these are normally used so F is not sold.
Occasionally BA has to swap planes around and you end up with a 4 cabin plane flying a route where Business was the highest cabin sold. Normally First is left empty but if there are not enough Club World seats to accommodate all the relevant passengers then the First cabin is used although it is CW food, drinks, amenity kits etc.
The risk is that if you are currently in an F seat but on the day of travel there are enough seats to fit everyone in CW due to no-shows etc. then you will probably be moved to whatever seat is left in CW. Some people advocate keeping a decent CW seat over rolling the dice on an "upgrade" although I see in your case you didn't move yourself forwards.

If your flight is imminent then it then it may well now be under airport control so call centre staff won't be able to shift you. I'd suggest keep trying on App or MMB and failing that check-in a little earlier than normal at a desk and ask if the flight is full and you can stay in your F seat or if not move to a preferred J seat.

Search for FLUB on the forum to see further threads that may be relevant