Brassgirl - You should try to get a hold of the Northumbria Anthology, which contains dozens of Teesside & Tees Valley songs. It's expensive, but worth it. Check out the website:
http://northumbriaanthology.com/

As for the Cleveland-Yorkshire debate, I've known some people get really bent out of shape over this (why I don't know) but it was first named Cleveland by the Angles (Cliff-land) which would have been before the Vikings renamed Eboracum "Jorvik" which was of course glossed to York, and the county was cut away from the Kingdom of Northumbria later still.

I went to school in Darlington (mid 60s) when Teesside first became designated a city, and the kids from that neck of the woods were proud to have their own city. Also to have Stan Anderson lead the Boro into the old First Division. ;o)