The Williams crankset that Jerry just bought appears to be the C34 model hwich was jusy about the most popular and affordable of the manufacturer's range. Depending on the thickness of the crank itself it might be the 1000 model...this was slimmer and more expensive. The C34 was the workhorse of Williams range and could be found on all manner of bikes, including Baines...but it tended to be used on one's everyday bike, rather than one's "best" machine. It was available as a double, but the discerning rider would probably have chosen the Williams C1200 which was a much more elegant design..and available in the "normal" tooth sizes of 46/49, 47/50. 49/52 etc. Jerry's c'set looks as though it might have been part of a tandem set.
In the early 50s there was a tendancy to use chainsets such as Agrati, Durax, Stronglight, Simple, Duprat etc or sometimes Chater-Lea if an English brand was preferred.
The Huret Alvit wasn't available in the early 50s..so we used the Huret Tour-de-France, or the Simplex version, or the Super Champion Osgear. For an English-clad bike, there was the Cyclo Ace, or the Benelux (very popular)..and Campag's Grand Sport came along in 1952/3 ( I think it was around then) but that was generally too expensive for most of us. Sometimes the Constrictor gear was used, along with that company's other accessories such as its hubs, rims, pedals etc.
As for brakes, the Weinmann Vainqueur centre-pull was later, sometime in the 60s...but the very highly regarded 730 side-pull was sought after at that time. Other brakes that were popular were Lams, CLB/Alps (with their very elegantly cast curved levers and hoods), not forgetting the Universals and of course the Balillas. For the strictly British brigade the GB Duralamin was much used..and slightly later, the other GB models.
The discerning club cyclist would mix and match his accessories by picking the best of the European "crop"...but from memory..and I lived not far from Baines shop in the centre of Bradford and its workshop at Idle, ... most Baines owners would follow a traditional route and use an all-English mix..including, of course such hubs as Blumfield (excellent stuff) Harden, or BH Airlites...or the exotic Shellwins or Powells..on Constrictor or Dunlop rims.
If you read this contri early enough and then search through Hilary and Peter's current Ebay offerings..you could put together a very representative bike.
Good hunting
Norris Lockley, Settle Uk