I'm a little confused here. If, as stated, it is a Birmingham gun how would it have "London fine rose & scroll engraving"? It just doesn't look like a 6K gun to me.
Just Curious, George
Always be willing to read "London style" where "London" is written. The engravers in London were certainly not the only ones capable of such work. Birmingham would have been chock-o-block with men who could have accomplished this engraving. People get a little over enthousiastic about associating London with various aspects of guns.