I have a 1957 BSA Imperial Featherweight. The rifle has the ring and bridge cut with a 19mm dovetail to take a proprietary Parker-Hale ring set. It's a simple dovetail (not double like a Weaver or Picatinny) with a vertical dowel in the bridge to take recoil.
After three months of searching I was unable to find a set of the correct Parker-Hale rings for my rifle and scope, but I did find a message someone left about being able to use some Warne rings. So I called Warne a while ago and talked to one of their Randy at Warne, who knew all about the BSA and what rings fit.
They sell a kit with two CZ550 front rings to fit the BSA.
Randy said some BSAs don't have the dovetails on the ring cut all the way to the front; for those, the end of the dovetail acts as the recoil stop. Mine's cut straight end to end, though.
Warne makes that particular CZ ring in 1" or 30mm, and in "medium" (.425" high) and "high" (.535" high). They measure the height from the dovetail to the bottom of the ring, so add .50" or .59" to the centerline of the scope tube. They don't make a short ring for this application. All current production rings are matte finished; they're phasing out gloss finished rings.
Randy said Warne doesn't have a part number for the two-front-CZ-ring kit, so you can't order through their usual distributor network. But they'll sell you the correct rings directly for $58, plus shipping. Expensive, but 1/2 to 1/3 the price of the "correct" Parker-Hale rings, if you can find them.
My scope sits a bit taller in the medium-height than I wanted - my scope has a smallish objective - but the rings fit the receiver just fine; the BSA and CZ dovetails apparently have the same dovetail angles.
The CZ rear ring is supposed to have a square block that interlocks with a matching divot in the receiver to keep the rings from sliding with recoil. The Parker-Hale rear ring had a round dowel. The CZ front rings just clamp on, with friction holding them in place. I'm going to shoot the rifle a bit to see if the scope stays in place; if it shifts, I'll drill the rear ring for a PH-style dowel.
The P-H rings are apparently in short supply because they're the correct rings for some SMLE sniper models, and the SMLE collectors vastly outnumber the BSA owners.