I was only kidding. There was a British singer a few years ago who tried to make it in the US and came back with the most laughable hybrid accent that she was blatantly putting on. I'm sure yours was more cute than laughable. Isn't the stereotype of Americans loving British accents true?
Not, unfortunately, in the Nebraska village where I attempted to start my ministry. I was told I was "flaunting" my having studied in the UK and purposely putting people off. It was a load of rubbish, but what can you do? One of the funniest moments for me came when I was making a tour of the Continent. I was in a bookstore in Ravenna, Italy, between trains and trammelled with rucksack, purse (a document case, actually), camera bag, and so on. The proprietress, annoyed at how long it was taking me to come up with the money for my purchase, threw up her hands and cried out, "Mama mia! Inglesi!"
Back to the original post . . . I have a lot of these interruptions in my WIP; perhaps too many. I struggled with how to present them, and after a lot of thinking and research, settled on this: “I would love to come with you, but—” she stubbed out her cigarette violently—“I have to damn well work, don't I?” I pasted that from my word processing program. In it, if you space after -- and ---. you get a nice, linked-up en- and em-dash, respectively. The middle one would not be correct, because it makes the cigarette-stubbing into a speech tag, which it is not. The third one is fine. A lot depends on whether the action goes on at the same time as the speech, or if it interrupts it. Nice bit of byplay, that line, incidentally. It says a lot about the speaker and about the one she's speaking to.
I had settled on my first form, with the em-dashes. I should do another editing pass to ensure I have been consistent.
“I would love to come with you, but—” she stubbed out her cigarette violently—“I have to damn well work, don't I?” I wouldn't do the above. I would only use the dash if the speaker was interrupted by another speaker. (also, why the question mark at the end? The speaker is not asking a question, she's making a statement.) "I would love to come with you but—" "I know," Sarah interrupted, "you have to work." "Shit, isn't it?" Paula added and violently stubbed out her cigarette.