Does anyone know if it's open at the moment? I understand it recently moved. To be honest, I only heard of it a few days ago; I was reading Geert Mak's In Europe, a wonderful book (albeit one too large to hold comfortably), and he eulogizes it and I thought that since it's within walking distance of home I ought to visit.
The museum has moved a couple of doors up the road into the Old Town Hall at 151 Walworth Road.
It is certainly worth a visit to see the curiosities of the Cuming family collection and the Southwark local history stuff.
Unfortunately, Southwark's art collection, formerly housed at the South London Gallery, has to fight for space in the new temporary exhibition gallery with other shows, and I think that very few items are currently on display. (The selection they included in the opening exhibition last year was a rag bag - including some very fine stuff of all periods, but a disproportionate amount of the space seemed to be taken up by big pictures painted in the 1960s by British artists who [IMHO] showed why they are quite justly neglected nowadays).
There is no indication yet what the autumn show in the temporary exhibition space will be. Previous temporary exhibitions at the old venue included some extraordinary displays from the Cuming ethnographic collection storerooms - which contain little known items going back to the voyages of Captain Cook.