There are two different versions, just to complicate matters:
The manual cable layer (which I think is the one in the photograph because that has a Barrows, Drum, Mk.4 (or similar) visible) which can be used in the vehicle (I think) or lifted out and operated on foot by the line party.
The mechanical cable layer. (At least one of these was engine-driven
and propelled the cable out of the side of the vehicle, controlled by the operator using a foot pedal (and, I assume, a hand throttle for the petrol engine that powered it). This was intended for rapid line-laying along roads, either feeding the cable into hedges/ditches, or into the street gutter in towns/cities where the line party would tie the cable off to drain gratings as it was being laid.
I suspect that all the information you need is in Signal Training Volume IV for the appropriate era, either the 1927 edition or the 1941 reprint and the pamphleted add-ons to that. Another possible document for the actual use of the kit is the London Division Signals (TA) training manual from 1939. (Only look at the Indian version of Volume IV if you intend laying cable from an elephant.
)
The photograph shows a line party equipped for 'Poled Cable', and looking at the picture I suspect they're reeling-in an existing line for re-use elsewhere. (I can't see any other reason for so many of them holding poles and someone operating the drum barrow. Unless the whole thing is posed, of course.)
The truck has a ladder rack and storage for the standard 18-ft two-piece poles for overhead line and road crossings. Other kit would be a sledge hammer and 'jumper' (a pointed steel bar used for making holes to stick the poles in), picks and shovels for buried crossings, and the usual cable jointing tools and supplies. Everyone has a lineman's belt with a swivel loop to hold a clasp knife and a belt frog with a pair of of pliers in it. (The knife for cutting spun-yarn to use for tie-backs and for removing cable insulation and scraping the wires clean, and the pliers for cutting cable and twisting the joints on thicker cable, etc.)
Chris.