Hello Cat,
As luck would have it I’ve just come back from walking the Cleveland Way and we camped (almost) all the way. However, we didn’t do the Tabular Hills Link back to Helmsley so I can’t help with that bit.
My first piece of advice would be to ring up the National Park people and get a copy of the accommodation guide. The number is in the back of the national trail guide, but I can post it here if you like.
We camped on each day except the first. I couldn’t find a camp site handy for the top of Sutton Bank. So we spent the night in a caravan in the back garden of a B&B near the Hambleton Inn (Although the very kind lady would have allowed us to camp in her back garden if I’d wanted to. So I suggest a ring round the B&Bs).
Other places we camped were: -
The campsite near the youth hostel in Osmotherley.
Beak Hills Farm (about half a mile from the path between Carlton Bank and Clay bank – this is the tricky day for finding accommodation, but we did get a free lift to the pub!).
Park Farm in Kildale.
The campsite in Saltburn.
The campsite at Runswick Bay.
A farm at Robin Hoods Bay.
Scalby campsite in Scarborough.
All of these were in the accommodation guide. If you need any more advice let me know.