London Air Travel » British Airways » British Airways Fleet Plans »

Every year the parent company of British Airways, International Airlines Group, publishes an annual fleet plan at its Capital Markets Day.
Here’s the latest fleet plan published last November:

As this is published for the group as a whole, it’s not easy to distill which orders and future deliveries relate to BA, particularly for short-haul aircraft.
However, BA has just filed its own annual accounts. We read these things so you don’t have to, and here is BA’s plan for new aircraft deliveries as at 31 December 2018:

This does pre-date IAG’s decision to order 18 Boeing 777-9 aircraft for BA. Although it includes one wet-leased SAAB aircraft, it doesn’t include others such as Air Belgium’s Airbus A340. BA CityFlyer is also due to acquire an additional (presumably second hand) Embraer E190 aircraft for London City.
Taking this into account, planned deliveries of new aircraft are:
Short-haul
Airbus A320neo: 18, with options for 33. 3 have been delivered this year.
Airbus A321neo: 9, 2 have been delivered this year.
Long-haul
Airbus A350-1000: 18 aircraft, with options for 36 more. 4 will be delivered this year.
Boeing 777-300: 4 aircraft, to be delivered in 2020.
Boeing 777-900: 18 aircraft, to be delivered from 2022 to 2025.
Boeing 787-9: options for 6 more aircraft.
Boeing 787-10: 12 aircraft, to delivered from 2020 to 2023.
In total, that’s 52 new wide body aircraft over the next five years so, to replace at least 35 Boeing 747 and 3 Boeing 777-200 aircraft.
This does allow for a substantial amount of growth, but is of course subject to change depending on economic and geopolitical events.
On other point of note is that BA’s options to acquire a further 7 Airbus A380 aircraft have now either expired or been cancelled. Following the decision by Airbus to end production of the Airbus A380 it has been clear that BA would not be ordering any more new A380s. This is now beyond any doubt.