True. There is, however, a Northern Irish Accent, a Scottish accent, a Glasswegian accent, a Yorkshire accent, a Welsh accent, a Working class accent, a cockney accent, a posh accent... lots.
i think the one most people think of as a British Accent is a half-way mix between a posh accent and standard middle-class english.
It's perfectly acceptible to call them all british accents, though. Can you distignuish between a Cantonese and Mandarin Chinese accent? Or Swahili and Affrikans?