Thanks for an interesting image, Pedrocut. These men would all have been members of the 6th Warwickshire (Sutton) Battalion. Very regrettably the 1941 Officers' List, which has been published and is a very useful method of tracking down individual HG officers in every battalion), is incomplete as far as the Sutton unit is concerned. And so I can't check on most of the names mentioned. Capt. Bigwood, however, definitely became a Lt.-Col. which was the normal rank for a Battalion C.O. from early 1941 and commanded thereafter. "Lt.-Col. Strevens" bore a strange rank for an "Administrative Assistant" - that may have been his Great War rank but he would not have maintained that later. He may have been the Battalion Adjutant. Similarly with Messrs. Holte-Smith, Gay and Hollands. All the "Misters" would have been given proper ranks within weeks.
Not sure of the extent to which a mounted unit like this represented a normal activity during the 4-and-a-half years of the Home Guard's existence, even over such appropriate terrain as Sutton Park. It certainly represented a good "photo opportunity" but I suspect that the every day work of these men was much more to act in a conventional infantry role - observation, patrols, guard duty, establishment of defensive positions, exercises - and training in every conceivable technique required by an infantryman.
It would be very interesting if any member can throw further light on the men shown and their HG service.
Chris
(Edited: Battalion number subsequently corrected)