here are the BA regs on hand luggage -- note that you can take two bits of hand luggage now (useful for you, I should think!). Virgin appears to be one piece plus a handbag at the moment -- I note that it's amazing what you can fit in a sufficiently large handbag in terms of books -- and AA looks like it's just one piece of carry-on.

I personally don't mind Heathrow but then we live about equidistant from Heathrow and Gatwick, and Luton and Stansted are an utter pain in the arse to get to (easier to go from Southampton, for heavens' sake)