The fixings that I took out of the walls when I was deconstructing the seats were held in place by special pop rivets. I couldn't get my hands on these, so my brother made some for me. These are the ones I took out:

And here is how he made a similar item.

First get some 5mm diameter rivets. The body of the rivets are about 20mm long, he got them from a lorry garage and reckons a bus garage will have them too. You only need a few so it shouldn't be too hard to wheedle a handful out of them if you ask nicely.

Set the rivet in a vice or the jaws of a workmate (Black and Decker workmate that is...not one of your actual workmates"). With a fine disk on a Dremel, or similar hobby tool, score four lines along the length of the rivets body...evenly spaced around it...north south east west if you like. Now when the rivet is squashed up the sides will split and get a grip of the plywood from the inside.

Two final tips...they rivet gets very hot so watch your fingers...and if you see sparks flying it is because you are scoring the steel nail on the inside of the rivet...save your disks and dont go so deep.

And finally the finished article almost completely closed in the pop rivet gun...notice how the sides have split and will continue to widen until they grip the inside of the plywood wall.

If these rivets hadn't been available I was going to try the plasterboard fixings that you get for cavity walls. I think that might have done as well, but this was more fun!