I honestly can't remember. I was one of the first to join Privium, but citizenship was not an issue for me. Their website currently says:

"You can only become a Privium member if you are in possession of a valid passport or European I.D. card from a country within the European Union, or one from Liechtenstein, Switzerland, Norway or Iceland. If you are an asylum seeker or refugee you are unfortunately not able to register as a Privium member due to limitations set by the Royal Netherlands Marechaussee."

Anecdotally, from visiting the lounge pre-Brexit I got the impression that Privium used to have a lot of members from the UK. At certain times of day there would almost be enough very British suits in the lounge to almost fill an entire Club Europe cabin to LHR.

Johan