That looks like a really nice English frame. I just bought one myself from Hilary Stone in England, and it has the same dropouts as on yours, both front and rear. I think that you'll find the rear dropouts have a Simplex mark. My project is an F. W. Evans (London shop) frame, purported to be from the 50s. I'm pretty much in the same boat as you, paint-wise; but already decided to have it done. You'll probably find that the head and seat tube have angles about 71.5 degrees or so; pretty relaxed. And maybe fairly long chainstays, like 44.5 cm or so from BB to middle of the rear dropouts.
What I'd do, provided that the brakes will reach 4 mm farther than they did previously (one looks like it will, the other maybe not) is to outfit the bike as a 700C-wheeled single-speed and try out the ride that way; minimum of investment and adjustment, you're not stuck with 27" tires, and if you don't like it, you could always sell the single-speed wheelset later -- they're pretty popular. If your rear (the usual culprit) brake caliper doesn't reach, then no problem. Weinmann made both "610" and "750" calipers, pretty much for this reason. The former (like what you have two of) have nominal reach of 61 mm, while the latter go to 75 mm. They were ubiquitous in the 70s, and there are plenty of them available in bike coop bins, and on eBay. With a fixed cog (rather than freewheeling single speed) on the rear, you could even dispense with the rear brake, since you can brake the rear by "back-pedaling". But I'd go for two brakes and a freewheel. And use Kool-Stop thinline brake pads for excellent stopping.
BB-wise, it's going to be English threaded, so any sort of bottom bracket will fit it, except maybe some super-weird modern stuff: either cottered (what you have) or a square-taper type. You can get a cartridge-bearing BB (easy to adjust, like IRD or Tange) and a single-speed crankset (Origin8 or the like, with a 46T ring) for not that much outlay. Somafab.com has all this stuff, as well as any well-equipped bike shop, or other e-tailers. It might be worth having the BB housing "chased and faced" by an expert bike shop, especially if the faces of the BB shell are mucked up by less-than-knowing disassembly.
Depending on what your ambitions are, bike-wise, you might decide that a carbon bike is your cup of tea, and the Mal Rees isn't. That's OK; more bikes for us vintage fools. Just don't f__k it up for us, if you know what I mean!
Last edited by Charles Wahl; 10-06-15 at 08:24 PM.