I can’t really add any clarity other than offering some more detailed history on Midlands. Possibly the L is for London for their London office, but just a guess and no proof at all.:
Here is a brief IGC break down on the history:
"The Midland Gun Company was established in 1888 at 77 Bath Street (Demon Works), with additional premises on Price Street. Founded by William Baker and Arthur Marsh with intentions to compete with others, such as BSA, for good quality economically priced machine made guns.
By 1902 the company was owned by H Ludlow England who, in that year, bought Holloway’s shareholding in Holloway & Naughton.
The company may have left the Price Street works in 1890 and moved to 81 Bath Street, but in 1900 they were recorded back in Price Street (at No. 81?). These and some subsequent changes of address may reflect changes of the principal offices of the company rather than actual acquisition and disposal of premises.
In 1910 the company was recorded at 77 Bath Street, and by 1930 it had taken over the adjoining property of 76 Bath Street. It seems that by this time the factory was called the “Demon Gun Works”; the company had adopted a naked male demon as its logo (engraved on the butt plate), they applied the name “Demon” to their top grades of guns and cartridges.
At about this time (1930) the company had an office in London, and they sold a wide range of guns, pistols and shooting equipment by British (BSA rifles) and foreign manufacturers. They had a small wholesale export market, and they made components e.g. actions for the trade.
Between 1937 and 1945 the company moved to 74 Whittall Street, but it may have retained the 77 Bath Street premises.
In 1952, the company, then a shadow of its former self, was bought by Parker-Hale. Some reports say that the company traded until the early 1960s, other older reports state that Parker-Hale continued to use the Midland name on its guns up to about 1970."