Leather
Wipe with a barely damp cloth the day the dirt happens, not the next weekend. A dedicated sneaker cleaner (Jason Markk, Reshoevn8r, Crep Protect cleaner — all easy to buy in the UK) beats washing-up liquid, which dries the finish. Stuff the toe with paper while it dries, away from a radiator. Heat cooks glue.
White leather yellows if you leave it wet in the sun. Dry it in a room, then use a white-specific cleaner on the foxing, not on the suede overlays.