Apologies if I missed mention of any of these earlier, but here's a few I've thought of (not sure why we're doing this but what the hell):

Song of the Clyde
Go Little Swale
Land of Three Rivers (refs to Tyne, Wear and Tees)
Fog on the Tyne
The Coaly Tyne
Waters of Tyne
The Kent, The Keer and the Lune
Ferry Cross the Mersey
The Miller of the Dee
Pill, Pill (Avon)
The Leaving of Liverpool (Mersey)
I Wish I Was Back In Liverpool (Mersey)
Anna Liffey
Summer in Dublin (Liffey)
Irwell Delta Blues
Aloha Severn Beach
Cousin Jack (Tamar)
Roots (Tyne and Tamar)
Three Score And Ten (Humber)

That'll do for now. Bit of a mixed bag - sure I could think of more given time :)