I went looking for one some years ago. I did a lot of research and I looked at 3 or 4 cars and didn't pull the trigger.
I found, with the possible exception of the convertibles, that they are not like other "classic" cars. People don't generally restore them because the expense and difficulty would far, far exceed what they would be worth when finished. I mean, most cars won't return their restoration costs, but JI's in particular are a black hole. They are very expensive to restore and do not command much dollars as restored.
All the cars I saw were largely original, almost all with original interiors or maybe the front seats redone at most. They typically had some sort of modification (the MOPAR guys are attracted to them for obvious reasons) that didn't usually complement the car. Think shag rugs, vinyl or ugly covered seats, crappy hot rod paint jobs, etc. I was operating under the philosophy "buy the best you can afford" and couldn't find one that was very nice, though none exceeded my budget.
There aren't a lot to choose from. I found myself flying to a couple of different cities to look at them and always regretted spending the money on the plane ticket.
There are some parts that are very difficult to source and any bodywork is a nightmare because all the fenders are welded on the car. That back glass piece, for example, is tough to find.
When I was looking there was one guy in the NW somewhere that was a specialist and did supply things like the interior wood, etc. After watching one "restored" on Wheeler Dealers, it looks like Martin Robey might be making some parts for them in the UK, as well.
I drove a couple of them and they are beasts. Not particularly refined, but you get all the muscle with some British handling and interior work.
I gave up after a while and bought a Jaguar XJS instead. While they have their issues, I never had a problem with parts, support, etc., and it was a much more refined car for about the same money at the time. Very similar in concept to the JI.
I still think the JI's are cool, and might still want to own one some day, if I could find that elusive car that someone had restored and was willing to sell at a big loss.
Again, the convertibles are a different story. There are some restored ones available, but, of course, you pay up for those.