Duncan asked for discussion of parts choices for a 1961 Carlton Flyer with track-style ends but drilled for brakes--sounds like we're into 'path racer' territory. Peter Kohler offered a list of suitable parts.
I love this kind of thing--visualizing a parts mix ahead of time--so I thought I'd chime in. The hubs you've got sound very appropriate--are they a 32 /40 hole pair? Not that they need to be. Hm, what rims? Fiamme, Weinmann, didn't Milremo have rims on offer? Or any of a multitude of French and Italian rims. They could even be wooden rims on a trackish bike (we are likely talking about 700c tubulars, I would think, with those ends). Now, regarding brakes. I think it's along about this time that GB rebadged the Altenburger sidepulls that are dual-pivot, calling them Synchron. These are pretty interesting brakes no matter what brand name is on them. Centrepulls are generally my favorite, but for some reason I'm seeing Synchrons or script-logo Weinmann sidepulls on this bike (as I gaze into my crystal ball).
Here's a quote from a Carlton advertisement in the February, 1962 issue of the C.T.C Gazette: ". . .every Carlton is chosen by its rider for his own particular purpose. You choose one of the many Carlton hand-made models and select the components, fittings and features you require to give you a specialist machine; or you compile your own specification and Carlton build to your individual preference. Either way you get a very special cycle, yet the price need be little more than you pay for a good mass-produced one."
Don't forget Fiamme and Milremo...for bits other than rims, too, you know...and my crystal ball says Williams or TA for the crankset / chainset. Tell yourself that the bike had cottered cranks at first, but that in short order ('63 or so) the owner ran out and got the new TA arms. Or Stronglight 49 with TA rings. Or go for cottered steel, still.
Back to brakes--I love some of the slightly oddball, not-seen-everyday sidepulls with script logos: Balilla, Altenburger "Brillant"--even the Czech brand Favorit. If you're not carrying a lot of extra weight (like panniers), why not try some of these jaunty also-rans? The price is probably right. Put good pads on them and ride. Make hoods out of bar tape if need be--or improvise "honking rubbers".
Gee, I've learned a lot in the last two years--thanks in part to you all. Yet a lot of the knowledge just has to be trial and error.
I've got a '61-ish Carlton myself--capella lugs, model unknown--still a long way from built. Like Duncans it's one of my winter projects. Somebody sprayed it the color of Hank Marvin's guitar--"fiesta red", which I will re-name "Flingel Bunt's British Tomato" for any Shadows fans out there.
Good luck, Duncan!
Tom Ward New York City, just back from a gig in Benidorm (a long story)(Spain)
http://www.theblackdiamonds.net (not much to see yet, but it's a band)
http://www.thedansettes.com (my other group, backing up three female vocalists--a girl-group)