The brickyard “I now believe” was in St John’s Tunbridge Wells. This is because John Ready Thurston (my Great, Great grandfather) who lived at 23 Southfield Brickyard just a few yards from a brickyard, in the 1881 census he was shown as “occupation Brick and Tile Maker” also at 23 Southfield Brickyard was “William Boson, M, Head, married, age 29, born Frant, Sussex; occupation Brick maker's labourer”.
The Brickyard itself is now under the recreation ground – behind Hermes house.
John Ready Thurston came from Cambridge and moved to Tunbridge Wells with his family sometime between 1872 and 1881. John Ready died in July 1881 when he was just 44, possibly an accident in the brickyard? As his wife Susan re-married and died in 1919.
As to brickyard on the forest. I know they were there, but they would have been small operations.