Ellis Martin designed this cover with a border of wavy lines and usually a round Medallion Royal Arms for the One-Inch New Popular Edition planned for publication in 1940. There is Charles Close Society publication A guide to the Ordnance Survey one-inch New Popular Edition about these maps.

This was used in various forms for all post war maps. The original (1) had a Medallion Royal Crest that used hand lettering but later versons (2&3) used letterpress. You can see the Roman numerals VI in the G to the left of the crown. This is for George VI 1936-1952. The middle (2) from 1946 just has G and the third (3) from 1957 has no letters as Elizabeth the 2nd had come to the throne in 1953.
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3
Other colours were used. The Blue version (4) was used on quarter inch to the mile (fourth Edition) maps with national grid from 1945. The olive version was used on The Lake District, Jersey, Guernsey and Isle of Man maps from 1947. This one (5) is from a Jersey 2 inch to the mile map
(5)
There was also green version on a Guernsey map and a brown one on the 10 mile map
There was a Scottish version with the Lion Rampant - but only for the one inch map. Here(6) is a 1948 version (sheet 32 Lochboisdale and Eriskay) with GR around the crown and (7) a 1957 (sheet 54 Loch Etive & Glen Coe) without.
(7)