Hearing of his plans I had naturally volunteered my sledgehammer (best wedding gift ever - no household should be without one). Here I am switching from hammer to lever action, having loosened the side "wall". I'm using my leg to lever it away from the brick wall, ripping out nails in the process. But it's resisting.
Here I've switched to using a crowbar to haul out what I've just discovered is a wooden pallet with a few planks and some roofing felt tacked lightly onto the top. You can't see it from this angle but I'm not best pleased because the pallets - seasoned, solid and able to withstand rot and tonnage - are why it didn't fall apart the moment I started whacking it with a sledgehammer.
Pallets are very tough (they need to be) so pallet-built constructions can often be surprisingly solid. You can see how the side came out in a solid lump. Both sides came out with the pallets pretty much intact (fortunately the batons securing them to the wall had fallen to damp and insects). Once I had two pallets out the next step was getting them into small enough pieces to fit into a hatchback, wheelbarrow, or wheelie bin (our three disposal options -- the wheelbarrow belonging to a friend down the road with a bonfire space).
I started carefully taking apart the first pallet with the crowbar, but about three planks in, snapped and went back to the sledgehammer, dredging up the technique from some dim corner of my mind. It made for a somewhat splintery pile, but it would now fit in pretty much anything, as long as that thing didn't mind wood spikes and rusty nails, and wanted a pile of splintered old wood.
After all, we weren't saving the wood for anything.