I have just aquired two old (1960s) English 3 speeds. I know nothing about them, and only one has the old rear wheel. Considering rather than restoring the other, which is just basically the frame with cool cottered chromed cut out cranks I'd go fixed on it. Any ideas of how wrong this is?

Why not? Older bikes seem to have shortish top tubes, but if you can set it up to fit you give it a shot. Do you plan to leave the original handlebar, etc.?