Also, a few BA bookings I have for T5-T3 connections has resulted in receiving the following email from BA:

"Dear Customer

Due to a change in terminal, your connection at London Heathrow may no longer be possible due to an increase in connection times. We are in the process of reviewing your booking to ensure you can make your connection and if required we will look to rebook your connection/s free of charge on your behalf.

If you would like to discuss your options with us directly, please give us a ring on 0800 727 800 from within the UK, or +44 (0)203 250 0145 from outside the UK. If you booked via a travel agent or another partner, please speak to them directly to discuss arrangements for your booking.

We’re sorry for any impact this may have on your travel plans and thank you for your patience and understanding.
British Airways"