It's okay, I've got it now. I copied over a load of sections from the DNN web.config file relating to membership providers. One thing I also had to do was add a RoleManager key and set the enabled attribute to true.
sections copied...
Configuration/ConfigurationSections/SectionGroup name=dotnetnuke
... I removed all but the last 4 entries from this section for authentication, members, roles, and profiles
Database connection string, with database location modified as it is being accessed from a different folder.
Configuration/System.Web/MachineKey
Configuration/System.Web/AnonymousIdentification
Configuration/System.Web/Membership
Configuration/dotnetnuke
... Only the last 4 items retained for authentication, members, roles, and profiles
I could probably remove more than this but it seems to be working so all good...