And remember that BA does not have "FAs" - cabin crew is the preferred terminology.

I have certainly received small bottles of sparkling wine in WT+, however it was pretty grim. If it's a special occasion, there's nothing wrong with you bringing on a half bottle of proper champagne purchased in Duty Free and asking the cabin crew member (or the Cabin Services Director) if you could enjoy it on board, and ask if the could chill it for you.

Or pay for/upgrade to Club World; there's a sale on right now and 10% off codes are available.