Hey Bohdan, I have no problem with that, and would guess a British resident would use that construction more readily. It comes down to applying an older Germanic grammatical construction - negative follows primary verb - instead of adding the auxilliary "do". "We haven´t any single rooms vacant." actually sounds more archaic and formal. Throwing "got" into possessive sentences is relatively recent in English (same as throwing in "do", which was rarely done a few centuries ago), and sometimes I think it's a bit unnecessary and carelessly used. Sometimes it changes the meaning: "I have brown hair" means simply that; however, "I've got brown hair" sounds like you didn't have it in the past and recently acquired it. I suppose most people today would use the "we don't have any..." phrasing in both common writing and speech - the important thing is having only the one negative "haven't / don't".

...snip... I was a bit quick to jump to conclusions here, and I don´t want to misinform anyone, so I´ve edited this post. I believe Peachey here makes more sense than I did.

We haven´t any single rooms vacant. Although it can be understood, in general, it is not considered proper English. (At least not in the USA. -- I don't know about England)