Hi, welcome to the Forum and back to fly fishing,
Mullberry-Whin Chalk Stream near Driffield is available on a day ticket. (See my web page for details) and I believe that Ellerburn Beck at Thornton le Dale near Pickering also has day tickets. I would suggest you check with James at the Orvis shop in Pickering for clarification. The River Esk near Whitby is a Salmon and Sea trout river and is available on a day ticket. See web for details;
River Derwent. If you would like any more information or help with stillwaters, please email me thro' my web page.
Regards
gsflyfishing
GS Fly Fishing - Fly Fishing Tuition in Yorkshire