Just done the bit between Warkworth and Rothbury as 2 day walks, its an excellent walk, I did not notice any campsites.
Its mostly farmland, pastures and riverside walk , but you will also find yourself walking through woodlands every couple of miles or so.
No walkers about at all except to the east of Felton.
I don't have any specific camp places but if you camp late rise early ...
If you can not find any campsites camping in woods may be best bet as most open country is insight of farms, use google earth and have a look just west of A1 on route, and to south west of Weldon bridge etc.
The area south of Simonside hills southwest of Rothbury is wildish grassland/conifer forest so may go undisturbed here although the Simonside hills themselves are generally very busy with walkers.
On the coast as said a few campsites about or if not suitable maybe the dunes between alnmouth and warkworth, the kyloe forest north of Belford.
You will find yourself walking through/near quite a few farmyards, so could ask if ok to pitch, Terry Scott had success with this approach in Carry on Camping.
Edited: 30/07/2011 at 19:40