A fascinating bit of film. The formation sign is the 4 Corps running elephant chosen by Auchinleck. They were on home defence duties in southern England after the fall of France.
The Arm of Service serial looks to be on a horizontally divided two coloured background which must indicate Royal Artillery. GHQ Home Forces marking orders for 1941 show '6' (with corps bar above) as allocated to a Corps Troops medium howitzer regiment so these signallers would presumably be Medium Regt. Signals who would have been allocated 5x motorcycles, 4x 8cwt radio vans and 1x 15cwt plus 2x 30cwt lorries.
Indeed it is Lex. I have an 11 set and collected most of the equipment including the ground station antenna in the golf bag shown in that film. I really don't have much clue how to use it though Ron