There is no indication that it is a BSA, why then did the seller suggest it might be? Looking at his other items, there were a couple of large flange chromed steel hubs engraved with BSA and which probably came off this bike. The number 69224 isn't really a lot of use, it seems Raleigh and Sunbeam can be dated easily but not Dawes or BSA.
Once I had examined the frame and forks, and impressed by what I had bought, I had a hunt round for which bits could be used to turn them into a bicycle. I had taken a Dawes down the tip; 500 CroMo is actually quite a heavy frame, the tube is quite thick-walled - and the frame was far too large for me. However I had kept the wheels and the calipers. This BSA probably took 26 by 1 1/4 wheels, whereas the wheels that came out of the Dawes were 700C. I offered the front wheel to the forks and it fitted, the axle was 8mm and the hub narrow! It was the only hub in my garage that would fit the forks; it gets better, the caliper's drop was perfect for the 700C wheel and the drop at the back matched too, both with room for mudguards. In many cases modern bikes are built with wheel clearances far too close.
The seat tube clamp bolt was seized so I cut through it and could see that the seat post entry was not circular, gentle persuasion with a lever and the seat tube opened up
30/06/2016 I've done a bit more work on the frame and discovered damage to the left hand seatstay, looks to be filled with lead. Never mind, I don't think the seller knew, and it will still work - after all the bottom bracket threads are undamaged.
25/09/2017 The seat tube is actually 27.0 mm and I have a correct seat post fitted. I have removed the drive side LH bearing cup and cleaned out the crud. An aluminium sleeve was fitted to keep out dirt etc. but which restricted the new bearing cup, I removed it.
Also I had no idea the steering head bearings were so different, they have proved impossible to find on ebay but I bought a frame and forks with a full set. I prefer the BSA so it will get the set and I am considering machining a set from steel (and hardening them) for the other frame and forks. But we will see.