As much as I like to push the limits of my entitlement with the bike, wheeling a full size example around a supermarket would make me uncomfortable and tbh given how much the public inexplicibly hate us anyway, would very likely be seen as taking the pish.
Bromptons appear to be a law unto themselves however, and many (myself included) seem to have no issues wheeling them around in a mostly-folded state. I must admit yesterday as I approached the large, inviting Sainsbury's doors on the B, I was very tempted to just smash my way in and do a lap of the place - bet you could easily get away with it before anyone was willing or able to stop you. Probably not a very efficient way to gather shopping, however..