Taking your own seats may be more hassle than its worth and its likely that your car seat won't fit the 45 by 45 cm dimensions required. I have seen the infants seats BA supply and they look okay (also they fit the seat)
From BA's website in their information section:-
Extension seat belts and extra seats
An infant aged 0 to less than 2 years may sit on the parent or guardian's lap using an extension seat belt.
Alternatively, if an extra seat is purchased, an acceptable forward facing car seat may be used for an infant aged 6 months to less than 3 years. The infant child restraint device AmSafe System can be used for a child aged 12 months to 4 years.
For children over 2 years an individual seat is required.
Infant seats and carrycots
We can supply specially designed carrycots so that your infant can sleep on board, particularly useful for longhaul flights. We can also supply an on-board infant seat that attaches to the carrycot positions.
The carrycots and infant seats cannot be used when the seat belt signs are on.
We have a limited number of carrycots and infant seats, which are allocated on a first-come-first-served basis. Please request them from the cabin crew on board the aircraft.
The infants seats supplied by British Airways are:
ideal for ages from 6 months to 2 years, but can also be used from birth
adjustable to a variety of positions from horizontal to vertical
available for infants who weigh no more than 13kgs (29lbs)
available on all longhaul flights, except in First Class on Boeing 777 aircraft, where only carrycots are available
Car type safety seats
You may prefer to use your own car type seat for use by infants with a minimum age of six months to a maximum age of three years.
The seat must meet the following standards:
The seat must be designed to be secured by means of a normal aircraft single lap strap and face the same direction as the passenger seat on which it is positioned.
A purpose-designed children's car seat must have a 5-point restraining harness.
The car seat must not exceed the dimensions of the aircraft seat.
The maximum dimensions of the seat must fit into an area of 45cm x 45cm (17.5ins x 17.5ins).
Please note: Two part car seats, where there is the seat and a base are not suitable for use on aircraft seats.