BSA 240 Magnum recommendations?

Good luck. Tested mine shooting one handed, 10M style and felt a little torque. My only suggestion might be a match grip to make it more controllable. The 240 is designed as a sporter and fills that niche admirably. My recommendation is to enjoy your BSA for what it is and find yourself a true match pistol. Standard springers are not usually a good choice for controllability and match precision. There are a number of reasonably priced SSP or Co2 10M pistols that would probably suit your needs. Enjoy your shooting!
 
They're pretty rare in the states. Like a Webley Tempest they say it's fun to "learn" to shoot one well. I had a Tempest years ago and didn't keep it. And I never sell guns. For a reasonably priced gun that really shoots well. And is much easier to cock than a Weihrauch HW40 or Beeman P17 . And easier to shoot well. A highly underrated Gamo Compact(used $150). Or (same gun) new Air Venturi V10. I can find one for $260 . An SSP, I got one and slightly modified the trigger and was quickly shooting in the 90's consistently at 10m targets. I've had it about 25 years and still my favorite pistol to shoot. It was only $100 then! And it has a great big RWS sticker on the box. I can outshoot some guys with very expensive guns with it. LOL! The darn thing is just easy to shoot.