Yeah, the closest we get is some of our steak sauces, but even then, it would really only be brought out for steak. You could get a plate of sausage, chips and mushy peas in a nominally "British" restaurant here, and probably still get weird looks if you you asked for brown sauce. And god help you if you have a strong preference for something like the YR Sauce over HP.

Ironically enough, the English are somewhat dependent upon Irish enclaves around here for getting their fix of those sorts of things. So long as you can put up with some ball breaking, your best bet for consistently finding brown sauce is to find an Irish bar or restaurant that advertise showing GAA games. If they commit enough to be showing hurling matches, they'll probably have at least some Chef's and/or HP sauce.