The BSA seats have a couple of angles about 1/2 x 9" long to stiffen the base.
There should be supports, holding the rider weight to the frame. These come in 2 varieties.
On plunger frames studs/bolts that go onto the frame and have a round rubber bung (42-9183?) on top that hold the seat up right under the rider. Without these the seat collapses. If you look at the many A10s they look like this, even restorations.
Large rubber blocks (42-9057) that sit in brackets on the seat base, these are a slight wedge shape and sit on the side rail of the SA frame. Again often missing and seats collapse.