Hare & Hounds: Churchdown, Gloucestershire.

It turns out not to be Merseyside, but rather Gloucestershire, in the town of Churchdown...and the pub is still there too. This from Mark Lewisohn:
"As some readers of the blog have realised, the photo was taken during Paul and George’s hitch-hiking holiday. I have been sleuthing the day-to-day route of this original mystery tour, summer 1959, for the first volume of my Beatles History trilogy, out in autumn 2011, and this latest piece of the puzzle now drops nicely into place."
I was quite surprised by the number of similar looking pubs called the Hare & Hounds that seem to exist in the north-west and west of England (and Wales too, I dare say).
Anyway, thanks again to all who sent suggestions.