CLIVE replied:

Just returned from Arnhem land ruined city etc as orqaniser of club trip.
Your best contact is the Katherine northern land council,they can put you in contact with their representative in ngukurr.
Previously only certain tour operators were given permits but this is now changing.
Angela Rosas is most helpful at Northern land council in Katherine.
Best to apply early each year as only limited groups are permitted each season.-Good luck

Peter replied:

We were in Arnhem land in July 2002 and stayed and 4WD there for 14 days with many permits. "Permits coming out of our ears". All I can say "it is a very strange place- this is NOT for tourists - also NO-accurate maps". Give me your email in your reply-post and I'll email you directly. I wish someone could have given me some accurate infos before we went to Arnhem land!!! Our 14 days were OK, but the fishing was poor. Very poor in winter. The water was at 24 centigrades, far too cold for any decent fish. No( a trickle) spanish macquerel or barra in winter only sharks.