Found this, hope it's useful:
Wark Forest
The section through Wark Forest from milemarker 62 to 65 (PCW north map) has seen some work on the surface in 2002. This section is quite rough and NOT suitable for road bikes (unless you like fixing punctures!), the minimum tyre width should ideally be 28/30 mm. I have rode it whilst on the Trailblazing ride and was told there was 3 punctures out of the first ten to ride this section. Mountain bikes and well shod hybrids will excell on this section but there is really no realistic other way round so the skinny tyre brigade should exercise caution here.
Paddy O'Kelly has this to say ' First, I think it should be made clearer that the off road part through Wark forest is NOT suitable for road bikes. I did it on 28mm touring tyres and I'd say thats the minimum you should have. As this is the only off road bit for which there is no alternative, this section dictates the choice of bike, in my opinion. Some of our group tried on racing tyres and we had 2 punctures in quick succession'