The horses name is Invicta .Signals is Jimmy etc .
Originally the Home Guard were not permitted to wear the regimental cap badge until an ordnance was passed in 1941 (from memory).This can help date early photos . Anti Aircraft and Rocket batteries came under the control of the Royal Artillery and so Officers had the advantage of wearing white lanyards , RA buttons and whatever command arm patch they belonged to .The most notable being Eastern Command AA being the busiest (an upward pointing black archers arm bow and arrow on a red square patch . Woman officers in the Commands had different but equivalent ranks e.g. A Major (male) = Sub Commander (female) .
The early 3/8" wide blue NCO bands on the epaulettes were never withdrawn , neither were the HG epaulette sliders . These were sometimes worn by off duty HGs on civvy coats or the more clandestine units of the Home Guard as they could easily be removed for patrols in cold wet weather conditions when a battledress blouse was essential.But in general terms the normal Home Guard units took on the standard issue rank chevrons etc.
Guards berets with cap badges are often seen worn by Auxiliary Units as well as the more usual FS cap , but they were a completely different kettle of fish altogether ! Some units like the Upper Thames Patrol adopted unique dress based on Naval uniform with a UTP cap badge and the mounted Home Guard patrols (Horse ) adopted standard horse guard or despatch rider kit, puttees and leather bandoliers (RA primer belts or US issue 30-06) depending on rank but with the normal FS cap and county regimental badge.