Very nice!!
I agree with the others, what you have there is a comercial BSA no.1 Mk.3* regulated for target shooting. What makes it interesting is the fact that it bears both the A.G. Parker and Martin Adjust stamps on it. The muzzle end of the barrel may read "AG Parker Ball burnished" or something to that effect.
If you pull the forestock off you will probably find strips of cork acting as a bedding agent.
The real question is how does it shoot??
I'll bet it drives nails!!
Nice score!!