If we look at the title of this post, the original question was not did London "market" boxlocks. Neither was it about ejectors. " Moving the goal posts" in this discussion about UK gun history is not helpful but harmful.
This question at hand has been a topic of discussion for a long time and unfortunately it is not a subject that is easily decided as say a knowledgeable person of UK guns reading proof marks.
Many important issues are so important that they are only decided by empirical evidence by reasonable and knowledgeable individuals in a court of law and in a scientific environment; and this method is an established method that reasonable and knowledgeable individuals decide issues of importance elsewhere. This discussion to date has not decisively established that London gunmakers "made"( ".....that of procuring forged actions and barrel tubes from the trade, then filing or machining. boring, drilling, reaming, screwing and so forth required to "make" or build a gun or rifle during the period of about 1880 to 1950") boxlock shotguns and rifle with the exception of maybe Cogswell and Harrison. The Cogswell and Harrison exception is as a result as a member of the "gun press" of the day (circa 1900) recording what a principal of the Cogswell and Harrison firm stated about their workshop; however, there were no photos illustrating that boxlock gun production was being carried out in the workshop. This leaves the question are we to take what was written to be statements of a principal of the company to be absolute. It is known from the Cogswell & Harrison history published by later principals of the company (copyright 2000 by Safari Press), that Cogswell and Harrison had specific knowledge of boxlock guns through their extensive direct business interconnections with the Birmingham, England gun trade where boxlock (Anson & Deeley guns were developed and made daily); and it could be assumed by a reasonable and knowledgeable person that Cogswell & Harrison could have had employees in their London workshop gunmakrs that were Birmingham trained, qualified and experience makers of boxlock guns and rifles who could and did build/make boxlocks guns and rifles there.
We know that Mr. Harrison established somewhat nonconformist workshop methods in the Cogswell & Harrison that were not desired by the London trade such as less expensive ways of making parts and also the shoe lump barrel method of production on his best quality SLE versus using chopper lump barrels. So that he might also make boxlocks guns in his shop versus buying them directly from Birmingham could be in his business strategy and tactics.
To my way of thinking Cogswell and Harrison likely built some boxlock guns and rifles in their London workshop, but I have not in hand absolute proof that cannot be empirically disputed--which is what is desired.