Other than the basic HMV style, which was copied by most off brand manufacturers, I see no exact match for HMV products, in terms of the components or parts used.  Most of the components look like those supplied by Swiss manufacturers to the second tier companies.
There were a few online references to "National Band Gramophone Co." One shows a green version of the model you have -- 
http://www.gracesguide.co.uk/National_B ... mophone_Co  -- but provides no information about the company.
Doing a Google Books search -- 
https://www.google.com/search?q=%22nati ... 4&dpr=1.54  --  I noted that the earliest references is from 1938, and the latest is from 1957.  (There was also a mention  a 1980 edition of the Hillandale News, which profiled antique gramophones, records, etc.)
A children's version of your gramophone, dated from 1949/1950 appears on this page -- 
http://books.google.com/books?id=IzhXyR ... 22&f=false
There may be a few references to the brand in historic UK newspapers--not available online, of course--and other trade publications.  If I understand this correctly, the Gramophone Magazine -- 
http://www.gramophone.co.uk/news/gramop ... rchive-app -- now requires a subscription to access its archives.  Perhaps some member of this forum who DOES subscribe could do a search for you, to see if there are any references to the company.
Joe