Great find, but you might want to peddle it instead of pedal it.
I was amazed to find out what a decent vintage English three-speed is worth (and this one looks more than decent), but a lot more than I, personally, would pay. They are poseur bikes. Three-speed hubs, even Sturmey-Archer, which I presume is on this one, are notoriously finicky and complicated. The brakes won't work for sour owl shit, especially with steel rims, and especially in wet weather, although this one looks like it might have after-market brakes, hard to tell--what does it say on them? Weinmann? I would definitely get rid of the reflectors, no matter what, and probably the horn, with the idea of making it as clean and original as possible. I'm guessing that the cable housing, the grips and the cable clips are secondary, but that's a guess. Some upscale chrome clips would make for a cheap and effective dress-up. It also appears to be missing the seat clamp--I'd splurge for chrome there, as well.
But, no matter what you do, you will still always have a bicycle that is heavy and inefficient, even though it looks great. If you keep it and use it, you will always be adjusting the brakes and the shifting apparatus. If you keep it, I would suggest replacing the saddle with a Brooks leather saddle, if you can find one for a reasonable price, which will both look better and be more comfortable. The ones for upright riding positions cost $100 or more and wouldn't at all detract from the look. Naval jelly and steel wool can work wonders on cleaning up rust from chrome, not sure about painted surfaces.
I don't mean to denigrate this bicycle at all--I would've snapped it up at twice the price. I just wouldn't keep it. It's subjective.