Thanks, all, for ice cream and jacket replies.
Was just remembering the Milk Bar in "A Clockwork Orange"... and it was a rather wicked place. But I think it must have been sufficiently English for Burgess to have included it in his futuristic vision, yes?
Possibly a big city thing, though. London has so many eateries of all different sorts, it has quite warped my perspective of the rest of the UK.
Hello Auroral Light 
nice to see you
Yes, in hip ol' Cheltenham we did have a Milk Bar in the 60s and possibly it lasted till the very early 70s. It would be desperately uncool now of course, though if we wait long enough it will probably become a Retro icon and one will spring up in some modish place!
You are right that a 'milk shake' has no fizz so I misled you there. Ice Cream float must be the thing.
That sounds like a consensus to me. Enjoyed the sweet feedback, all.