Managed to sneak in some window shopping in London. Didn't find the specific badminton shops, perhaps I didn't research beforehand. London is huge, was lost in Bond street.
Managed to see some badminton stuff in Piccadilly Circus, particularly Lillywhites. Lots of Carlton badminton stuff and some Yonex.
It's pretty far from London, which I didn't have time to visit.
From what I see, Football (scoccer), Cricket, track/field, tennis are way more popular than badminton.