As others have said, make sure you check with your specific airline exactly what you're allowed to take on, and then double-check and check again. Airlines vary wildly in what they'll allow, in terms of both size and weight.
Funnily enough, some of the cheaper airlines can be quite generous with carry-on allowances - presumably because they're trying to discourage you from putting stuff in the hold. For example, Ryanair allows one bag up to 55x40x20cm, weighing up to 10kg. Easyjet allows one bag up to 55x40x20cm, with no weight restriction so long as you can lift it into the overhead bins.
BA is the most generous airline flying out of the UK, I believe - they allow one bag up to 56x45x25cm, weighing up to 23kg, plus (at most airports, but not Gatwick) a laptop bag, briefcase or handbag.
The stingiest mainstream airline I've come across is Alitalia; out of LHR they allow one bag up to 55x35x25cm, weighing no more than 5kg. But charters can be bad too; for example First Choice allow one bag up to 45x35x20cm, also limited to 5kg.
Did I say double-check with your airline?