The late 1940s RTTC timetrialists would not normally be seen out with a geared bike, afraid they might be mistaken for a road racer BLRC rebel. Yes it was almost a religious chasm.
The classic club timetrialist general purpose bike of the time would have been 73 x 73, (possibly 73 x 71) track ends with mudguard eyes, and wheel clearance for 27 x 1 1/4, bottom bracket probably 11 inches. The racing wheels were normally carried on the front to the event.
This Holdsworth looks like 72 x 69, the seat angle being a bit shallow for the time. I would say this is a bit unusual, many lug sets were still 73 x 71, and road racers probably had a 72 head, if they had a choice. The long fork rake is correct for late 1940s.
Keith