You have St Nicholas RPC in Chiselhurst. They have great facilities and cater for smallbore and FT/HFT.
http://www.snrpc.org.uk/index.html
Also have a look at the kent smallbore association (website currently down) to see other clubs that might be in the are.
Also there are a few in croydon area, list from the Surrey Smallbore Assoc
http://www.surreysbra.org/documents_clublist
Addiscombe won't be too far from you.
Hopefully there might be members living near you and can give you a lift. Or lodge a rifle at the club to save you taking it on public transport. Or carry it in a guitar case