off road van

You can, but the rangers will turn you around after you've driven for a couple of hours to get in there and send you straight back out again. AND, you have to go through the ranger station to get in. The signs say NO Caravans and they mean it.
You can store your van at Turkey Creek (Warmun) by either, paying full price for a site at the van park attached to the roadhouse, or, paying a small fee to have it locked away in a barbed wire enclosure over the road. Either way I would suggest that you book a site at the roadhouse for the night that you get back from the Bungles - it's usually packed out. There is another alternative which I wouldn't recommend - park it in the carpark on the highway opposite the turnoff to the Bungles.
I suggest you allow at least twodays to see the N.P.

Tessa

Hmmm, maybe they're stricter now than they were in winter 2003 when we towed our Kimberley in; perhaps they're tired of rescuing unsuitable trailers/vans (those without rotating hitches such as a Treg) which might have problems exiting some of the creeks etc.

When we were there in 2004 the Rangers were talking about excluding all towing into the park.
We left our off road van at the rest area outside the park for three days without trouble. It was securely locked with the coupling locked also. There were at least 6 other vans stabled there at the time.

We were there early this month and there were plenty of offroad caravans and camper trailers in there.I wouldnt like to tow some of the vans in that we saw there,that 50kms in is the the longest 50kms Ive ever driven.