I don't know about Hull but for Beverley here goes :-

Monday. Start 20:30 "Not The White Horse Folk Club" at the Forrester's Arms, Beckside. Folk Club
Tuesday. Evening about 20:30? Session at the "Sun Inn" Flemingate
Tuesday. Evening about 20:00. Easy session at the "Tiger Inn" Lairgate.
Wednesday. Evening 20:30'ish. Ged's Northumbrian & Irish session at the "Tiger Inn" Lairgate.
Friday. Evening about 21:00. Jo & Graham's session at the "Tiger Inn" Lairgate.
Saturday. Late afternoon? Short session at the "Sun Inn" Flemingate
Sunday. Afternoon, about 16:00 till it finishes. Session at the "Sun Inn" Flemingate
Sunday.Evening about 20:30. Irish session at the "Tiger Inn" Lairgate.

In Cottingham on Wednesdays there is the Cottingham Live Club Club

regards

Jake