Howard,
All I am going on, is the Contract number list, showing it and other contracts for that particulat type of trailer trailer as Brockhouse, confirmed by your plate with "J.B. & Co." which is J. Brockhouse and Company. During wartime there was co-operation between companies and it is possible that Dyson supplied the running gear for the trailer.
Looking at a copy of the War Office Data Book for Vehicles, dated 1944 and it shows similar trailers, 3 ton 4 whld for radar, ack ack, etc. as having 10.50.16 tyres, so the RL wheels would be a bit big, Bedford OY or Austin K2 would be the correct size. But if you really want RL wheels, contact Withams, who were breaking Green Goddesses and had RL wheels with good tyres for sale, 11.00-20 size.