Rode that bit today (686). Slicks would have been nearly impossible. Maybe if it doesn’t rain for a few weeks (in Kielder does this ever happen?) but otherwise it would be grim. The Forest Drive from the A68 to Kielder would work and is doable on slick. you could then pick up the lakeside way and head to Bellingham. (I did the entire ride below on slicks. The bits north of Newcastle (bloody bush) were hellish but it didn’t kill me, the bit from the lake is fine and really quite pleasant. So combine the lakeside with forest drive?
http://www.strava.com/activities/56223655#1442310113
You could try coming in through Kielder, Belingham and Wark on the road. Bits of it can be prone to racers testing their engines (particularly the road along the lake) but it generally quite a nice ride. The other option could be to follow the border and come in along the military road (probably worse for the racers as there are plenty of blind summits. My preference is the lakeside bit as is much nicer.
http://www.strava.com/activities/156338582
I do a fair bit of riding around those parts, so post if you want any help. This post was an inspiration for a ride up that way today so thanks 😉
http://www.strava.com/activities/236221888