The British tradition of fixed wheel riding harks back to a time when everyone rode fixed or three speed Sturmey-Archer. Even after reliable derailleurs came onto the market, fixed was still the low-maintenance winter training choice, which was cheap, good for the cadence and safe in bad weather.
By running an old Reynolds framed fixie, I feel in touch with that era. Toe clips (stainless) and straps (Binda)on good quill pedals, preferably with replaceable cages, seem appropriate for such a bike, along with a leather saddle and single enamel paint in a suitably retro colour, like, maroon, olive or black.
Some of those bikes from the fifties were wonderfully spartan, -quick, light and purposeful- and the mileages these totally committed lifetime cyclists racked up were amazing.........