I am not sure about this, but I think the definition of a Chalk Stream is not its clarity etc but the fact that the chalk acts as a sponge (aquifier) and mineral provider. Because the water for a chalk stream, by definition, is spring fed, the water not only remains very clear, it also maintains a stable flow and temperature as the reservoir of water stored underground in the chalk is a pretty constant temp.
Add to that the heavily mineral loaded water and you get ideal conditions for insects, which use the minerals and trace elements such as Calcium, Srontium etc in the construction of there "shells"/body.
So cool, stable flows and temperatures, minerals and clarity and you've got a little bit of paradise.
Driffield and Settrington Becks are the furthest North chalk streams.