I hope I can find a picture of a similar gun I just consigned to Greg Martin. #17476, Purdey thumb push opener, also with the London and Paris addresses. The dual cities markings seem to only appear on his earliest guns; some later guns carry two street numbers on New Oxford, London. Nigel Brown lists a numberr of his addresses, but not this dual cities marking. I think it is circa 1860 based on looking at a number of his guns.

Your gun, as is true of many of his products, has far more flamboyant wood than was utilized by his contemporary gun makers. I think it is one of the features which make Reilly guns attractive.