One of the important dimensions is the distance across the seat between the spring mounting studs on the underside of the seat, which should match the frame mounting points. Measure the frame with the rear wheel and spindle in place...the frames spread an inch or so in the raw. If the mounts are not directly in line, the springs will lean, and look a little ungainly from the rear, and tend to move the seat sideways as it deflects.
Another slight problem is the front frame seat mount is a pivot point, and if worn will allow the seat to wiggle sideways at the rear, which feels a bit strange. Further disappointment comes with the first pothole or speed bump, as the underside of the unchecked seat rail makes firm contact with your newly refinished rear mudguard, a precision dent if ever there was one. Some sort of bump stop within the springs is something BSA never considered.
The lower mounting for the spring was originally a threaded stud into the mudguard mounting lug, length and adjustment allowed to suit seat spring height and rider's weight. Homespun spacers for the springs may be required to end up with something that suits the ensemble.
While a single seat certainly offers a period look, I prefer the versatility of a dual seat, which offers a chance to move around a bit to keep the blood flowing on longer runs.
Swarfy.