This is Reilly SN 18677, auctioned off twice in the last two years and now for sale on Gunbroker. It has London proofs as usual and what appears to be a Purdey thumbhole under lever but there is no Purdey patent use number on the gun.
However, there are initials "WJ" on both barrels. There are three known Reilly barrels from this period with those initials. These must be Birmingham worker initials. Dr. Haus has been compiling a database of these initials.
But I've never seen the small initials and number "GNT 1232" with what appears to be a slide rule or hammer cartoon (and possible some faint smaller initials "WT" and "T"?). Can someone shed light on them.