Nappies R Us (NRU) do now have a 'showroom' at their main depot in Bolton, near Manchester in the UK
I would like to think I'd go an visit if I was nearby (I am planning a trip to visit friends in manchester soon), but I doubt I'd have the guts to actually go.
Sadly, there's very few places where an openly ABDL store would be tolerated here in the UK, and certainly nowhere near where I live anyway.
I used to live in London and there are places there where such a place could potentially work, but it would still probably need to be pretty discreet.
I'm thinking of somewhere like Soho, which is better known for its sex shops, red light zone, nightclubs, gay bars and super-expensive restaurants. I used to love just wandering around there, usually after a copious amount of booze, and indeed the entire district is awash (in more ways than one!) with inebriated people and often people (including myself back in the day) having to take refuge in some dark side street or doorway to go for a pee (or sometimes worse...)
Ironically, a diaper shop in Soho would be absolutely perfect - and judging by the sorry state of many a city centre these days, there's plenty of other places that should be actively encouraging people to wear!