Counter anecdote: I also have a British accent, and while I find Siri as shit as everyone else in this thread the dictation built into the iOS keyboard very rarely has a problem with my accent. I'm fairly close to Received Pronunciation, which I'd guess is one of the easier British accents for Siri to understand.

(I do often get frustrated with dictation quirks that don't have anything to do with my accent, like it choosing the obviously wrong option when their are multiple words that sound the same, especially its insistence on assuming I'm saying the name of a contact rather than the common noun that sounds the same.)