I've been wondering, in a case like this, could someone ream out the chamber partly a small amount, then put in a hardened steel striker plate?
Yeah. But...See cosmic's answer.
It depends how much time you wish to put into it. Relining or partially relining a chamber and recutting the chamber with a proper chamber reamer is about the be-all of fixes, if you can do it yourself, but the gun would really have to be worth the effort and cost if paying someone else.
I would suggest that relining the barrel is like to be easier, as you have fewer opportunities to get things misaligned.
Now, I dunno for sure, but I would take a close look at that firing pin/striker assy in the BSA, as I have seen a few of them, and do not recall seeing one that strikes the breech face when dry fired. The pin may have been replaced and made a little long.
Not such a big deal now, other than that he dent is there and visible. It might matter more if the gun was being shot competitively, as the movement of the case from the unsupported section of rim 'could' conceivably introduce some variability to the shot. In theory.
Sounds like a quickie cleanout with a chucking reamer.
Cheers
Trev