BA wanted to ditch First completely a few years ago. The problem was the First cabin on the 747 which is in the nose.
Taking out the fourteen F seats only allowed for one more J seat due to the design of that particular product.
They did remove F from a number of 777 aircraft.
Willie was a lot more optimistic on the future of First and has spent a considerable sum on upgrading this.
I think the F market is going to keep on shrinking and will be absorbed by an ever improving J class.