Many thanks for the info and kind comments, its like a jigsaw trying to get the history but im determined!! It doesnt make sense if the company was only at that address between 1888 and 1893, as my date marks are 1896-1904?
However after much research Ive found the following info which would hopefully explain the company history and the address narrowing the date made down to between 1896 my date marks & 1902 when the company moved from the address : (highlighted blue)
Kerr Armourers to the National Rifle Association. Sole Agents for Winchester. The firm may have traded initially as J Kerr, later as James Kerr & Co. They appear to have been established in about 1858 at 54 King William Street when James Kerr patented a 5 shot double action revolver No. 2896 of 17 November. In 1859 a further patent (No. 242 of 26 January) was for a similar revolver. In 1883 the firm moved to 118 Queen Victoria Street, and in 1887 to 114 Queen Victoria Street. From 1895 they traded as London Armoury Co Ltd. London Armoury Company. London Armoury Company appears to have been established in 1856 by Robert Adams and others (probably John and George Deane) to machine-make Adams revolvers at Railway Arches, Henry Street, Bermondsey. Initially, the comapny may have been a partnership. It took over the Deane Adams & Deane partnership's factory at 2 New Weston Street but from 1857 it was recorded as a limited company at Railway Arches, Henry Street, Bermondsey Street. In 1857 the company contracted to make interchangeable pattern 1852 rifles. In 1858 Robert Adams resigned (to establish his own business at 76 King William Street). In 1863 the London Armoury Company moved their offices to 36 King William Street and opened a factory at Victoria Park Mills, Old Ford Road. Robert Adams took over the factory at Railway Arches but two years later in 1865 was declared bankrupt. London Armoury Company took over his interest in John Deane & Son and the factory at Railway Arches. In 1867 the company went into liquidation and the factory at Victoria Park Mills was closed. The successor business, London Armoury, opened a factory at 27 Leman Street. Reportedly, the liquidation was caused by the cessation of orders from Northern states in the American Civil War. They had reached a point where they could supply their own rifles, and the company could not survive on the orders from the Southern states. At this time London Armoury had sub-contracted some revolver making to Pryse & Redman and Calisher & Terry. In 1875 London Armoury was sold to James Kerr & Co (Armourers to the National Rifle Association) and moved to Kerr's premises at 54 King William Street, but they continued to trade as London Armoury. In 1882 the company became sole agents for Winchester, and in 1883 moved to 118 Queen Victoria Street (with James Kerr & Co). In 1887 both businesses moved to 114 Queen Victoria Street and in 1895, whilst James Kerr & Co ceased trading in their own name, London Armoury again became a limited company and traded from that address. In 1902 the company moved to 1 Laurence Pountney Lane. In 1909 there was another move to 31 Bury Street, St James's where in 1913 they became agents for Colts Patent Firearms Manufacturing Co. In 1936 the company operated from 10 Ryder Street, St James's, but they had additional premises at 8 Bury Street which was occupied by Stephen Grant & Joseph Lang Ltd (it may be that William Robson had an interest in the business). In 1950 the company moved to 24 Holborn. In 1982 the limited company closed and the business changed it's name back to London Armoury, they moved to 639 Commercial Road. In 1987 the business was transferred to a new limited liability company. They were not recorded after 1991.