I thought I might just add a post-script to my earlier Contri on this subject..having just browsed through the Ebay offerings that I mentioned.
For the "all-British" purist, the choice of handlebars and stems was restricted, but Reynolds were often used as was the Strata range, including the extremely popular "South-of-France" model. Strata also made brakes and pedals, bottle cages etc. GB bars and stems were popular too. Other manufacturers of pedals included Webb, BSA, Constrictor, while saddles tended to be Brooks, followed by Mansfield, Lycett, Middlemore...
The more continental minded rider might chose Lyotard pedals, especially the platform model, Titan bars and stem from Belgium, or the popular Pivo/Phillipe French models, and Ambrosio were just becoming available from Italy. Nolicataneo (Spanish?) pedals were popular, as were Magistroni chainsets..as an Italian option to the Agrati.
Perhaps Jerry has his mind on a couple of bikes when he asks about Huret front mechs, as it never proved possible to put a double-chainset/front mech combination on a short-wheelbase Baines. If Jerry has another early 50s bike in need of a front mech. the choice was almost always the Simplex rod-type "front clanger" of the Benelux version. The lever type Hurets used by Bobet seemed to be very scarce in the UK.
Of the choice of exotic rims from Europe , AVA, Mephisto, and Fiamme were the most popular. Hope this helps rather than confuses..and I suppose what really matters in building up the Baines is that the accessories are period correct..the choice being very eclectic.
Norris Lockley..Settle Uk