Sheringham is 2nd Wed of the month at the Burlington Hotel. So you should OK for that one. Singaround format, songs occasional tune, mixed repertoire. There are a couple of othe places, Alby (last thu) and I believ Blakeny (last Sun) I don't know of anything else near Cromer during your visit.

There is regular weekly folk music in Norwich. The ones I know of are.

Sun, The Nelson, Nelson Street. Irish session - songs very rare.
Tue, The Nelson. English session. Possibly tunes only.
Wed, The Nelson, "Skiffle Pete". Seems to run as an informal singaround /folk club. Songs and tunes.
Wed, The Shed, Lawson Road, Irish session. No singing.
Thu, The Nelson, informal mix of songs and tunes old and new.
Fri, The White Horse, Trowse. Norwich Folk Club.