Wyler
You said "BA all the way" - if your whole journey is held under one booking reference - ie printed on one ticket, or on one e-ticket receipt, then you have no worries, as the airline is responsible to get you from point of origin to the final destination.
The only trouble can be if you put the two flights together yourself and booked them at different times, even though both bookings are with the same airline they will not guarantee your connection.
Hope this helps