BA themselves are not particularly problematic if you're travelling in a premium cabin, but BAA (who run/own LHR, amongst others) are very rigid, because max. sizes are set by UK government regulation. These are:
Cabin baggage must be no larger than:
• 56cm (22in) tall
• 45cm (17.7in) wide
• 25cm (10in) deep.
These sizes are overall, including wheels, handles and external pockets.
If you're boarding any flight at LHR with baggage larger than this, it's less hassle to check it before you go through security. They're almost certain to make you go back and check it anyway.