Translation:Don't worry; it's fake fur.
It is certainly not "perfectly" acceptable in British English, and I am not convinced that it is acceptable at all:
So far as I can tell the few occurrences in the .co.uk domain of the web are nearly all accounted for by poor translations for Chinese goods on Amazon UK and the like.
The term "false fur" has never gained any traction in either British English or American English.
"Fake fur" first started to gain traction in the nineteen thirties, and overtook "real fur" circa 1965.
"Faux fur" first started to gain traction circa 1987, and overtook "real fur" circa 1996, then overtaking "fake fur" in 2015.
Source: Google Ngram.