ok, I see...
so in British English the expression there didn't use to be is the correct one, isn't it.
I agree with Jeromed and the BBC. It's not an American/British thing, the use of "used" instead of "use" in that sentence is simply incorrect, although it's quite a common error made by native speakers, probably because in conversational English "use to" and "used to" sound almost indistinguishable.
Shouldn't this be There didn't used to be?
Never heard of it, and unrelated to there didn't use to be.
Because it's wrong.
I understand the contraction usedn't (used not) however the sound of usedn't is very close to isn't and if someone were to say it, probably you wouldn't know the difference.'Usedn't' is not wrong. It is very uncommon, even in BrE, but as gengo commented, it's 'used not', just as 'hadn't' is a contraction of 'had not'.
1) There used to be trees there, didn't there?
2) Didn't there used to be trees there? (colloquial)
The question is, is it correct in a formal setting?