I've just found this, which doesn't really help much:
http://www.portsmouth.gov.uk/media/Penc_Upload.pdf
Brighton Street
Runs north from Crasswell Street to Commercial Place
Crosses Church Path North
None of those roads are on a current map!
There are quite a lot of references to the various joining roads on that site, but it's making my brain go fuzzy trying to take it all in.