It's a gloriously dated specialist umbrella shop.
Hey, just a moment, wasn't I looking for a specialist umbrella shop?
Indeed I was, and indeed they had just what I wanted. I asked the man who served me whether my chosen brolly would be cheaper if I waited until it stopped raining, and he said, "of course, sir". I bought it anyway, and promptly dropped it when I stepped outside the shop. It still seems to work, though.
James Smith and Son have an Internet site, but in keeping with their "gloriously dated" philosophy you can't actually buy men's fold-up travel umbrellas off it.
I like that kind of quirkiness.