Ice cream is usually available in Club Kitchen as well, although quite often it's no longer ice cream but just chilled cream
For something different a short haul QF flight I was on the other day served ice cream on a stick in Y some time after the meal. I thought that was a bit different - I usually see ice cream in a tub on aeroplanes and not on a stick.
Some time ago I was on a QF domestic flight which was described as serving "supper". The alleged supper turned out to be a Cornetto (or the alternative supper, which was an apple). I never would have considered a Cornetto to be a supper. Maybe 5 Cornettos, but not one.
So, I'm in a way glad that BA doesn't serve ice cream to everyone. Can you imagine the uproar if BA replaced the afternoon tea with a Cornetto?