Very clean example of a MKII, a BMB 1941 dated shell with a mint 1940 dated liner, size 7, makers mark is not clear but has a M visible, so probably BMB same as the shell. Obviously it has been overpainted at some stage, hopefully wartime and its very clean condition which is matched by the liner suggests that it was period done. It has a greenish MKIII chinstrap fitted which is fraying and degraded but is otherwise very clean and matches the condition of the rest of the helmet.
There is no sign it ever had a logo on it, and I assume it was intended to be for a Warden or similar.

Click to enlarge the picture