Ages ago it used to be a very strict one bag policy at Heathrow.
Now it's a 2 bag policy dependent on your airline.
As you are travelling with British Airways, you are entitled to bring 2 pieces of hand baggage:
Your main piece of hand baggage is up to the dimensions 56cm x 45cm x 25cm (22in x 18in x 10in), including the handle, pockets and wheels.
Your second piece is up to the dimensions 45cm x 36cm x 20cm (18in x 14in x 8in), including the handle and pockets.
See this for further details:
http://www.britishairways.com/travel...n/public/en_gb