The Brown Brothers' Cycle Catalogue is a good place to start: oldroads.com - Vintage Bicycle Reference

Also, take a look at the Readers' Bikes on the Classic Lightweights website for inspiration: Readers' Bikes

A cyclist in the late 1940's would have had a huge range of components from which to choose. My personal choice would be:

1. Chater Lea, Williams, BSA fluted, Duprat, Stronglight, Durax or Simplex cranks and chainwheels
2. Chater Lea or Bayliss-Wiley bottom bracket
3. Simplex, Cyclo Benelux or early Campagnolo Gran Sport derailleurs (but you could also use a Sturmey Archer alloy hub)
4. Cyclo 4 or 5 speed freewheel, Reynolds chain
5. Constrictor Asp or Dunlop Special Lightweight rims
6. Harden or Airlite large flange hubs
7. GB Hiduminium stem and handlebars (although there are lots of others)
8. Chater Lea, Lytaloy, Constrictor BOA/Cobra, Webb or Allez! pedals
9. Brooks B17 with the oval embossing, with Reynolds or Stratalite seatpost
10. GB Courier brakes (the first generation GB brakes are a bit weak but the Couriers work fine)
11. Chater, TDC, Lytaloy or Stronglight headset

(Vintage brake cables and pads, tires, spokes and other small parts can be difficult to find in good condition so you have to use modern equivalents.)

This would be a period-correct build but if you're starting from scratch it will be time-consuming and expensive.

Things of which to be aware:
1. The rear drop-out spacing on early frames was about 115 mm so you can't use a more modern hub and freewheel unless you intend to cold-set the chain stays
2. Stick to British threaded components: pedals, bottom brackets, etc.
3. Make sure you don't buy parts specific to tandem bikes (Chater Lea bottom brackets can be a bit of a mine-field)
4. Early clincher racing rims use 27 1/4" tires which are still available but can be fairly low-end
5. Early sprint (tubular) rims are compatible with modern tubular tyres
6. Old equipment can be rusty and need a lot of TLC to get going; also cranks, chainwheels and derailleurs can bend over time and may need to be straightened
7. The worst aspects of very early bikes are the brakes and the gearing: I took a 1948 Hobbs on l'Eroica and spent a lot of time pushing it up and downhill

Hope that helps.