I fky on the shuttles quite a lot and prefer Gatwick to Heathrow because its easier to get in and out of but the 737 fleet is now looking rather shabby.
The one thing BA has going for it however is that despite the airframes and the shennanigans going on at the moment, they have the best crews in the business
Finally talking about age of BAs fleet the most memorable flight for me was on a Trident 3 in 1984 to Alicante (KTours charter) that aircraft used for the shuttle run then was the most comfortable I have ever flown on.