My approach to a build was a little different. I wanted an old-style steel tourer, 6-speed freewheel, and the friction shifters and related old components I grew up with. I wasn't interested in pristine cosmetic condition, I just wanted functionality with my own choice of components.
I picked up a Raleigh Royal frame with headset for £45, added a Biopace triple, Sountour derailleurs (inc lovely long-cage Vx rear almost mint), some NOS 27" wheels... etc.
The whole thing came to around £250 initially, to which I added £100 for a Brooks Cambium saddle. And it works beautifully.
I reckon my chances of finding a complete steel tourer with the components I wanted, all in tip-top condition, properly adjusted and spotlessly clean, would have been pretty slim.