I've found Prodlaw on the 1842 tithe map, in the township of Adderstone (parish of Bamburgh).
On a modern map about 3 miles south of Belford the B6348 leads west to Bellshill Farm. On the other side of the A1 there are two farms marked as Adderstone Mains and Adderstone Low Mill. On the tithe map whilst the former is Adderstone Mains, the latter is Prodlaw, owner Thomas Henry Graham, occupier Henry Dinning.
The farm seems to be Adderstone Low Mill on early OS maps too.
Added: Newlands Estate, Warenton, to the west north of Bellshill has the same owner and occupier as Prodlaw and Henry Dinning can be found in the 1841 census in the township of Warenton as opposed to at Prodlaw in the township of Adderstone.