Which county in England has the most castles?

Northumberland, with a total of thirtynine they are as follows:

Alnwick, Aydon, Bamburgh, Belford, Bellister, Belsay, Berwick, Blenkinsop, Bothal, Bywell, Callaly, Cartington, Chillingham, Chipchase, Cockle Park, Cotherstone, Coupland Park, Cresswell, Dally, Dilston, Dunstanburgh, Edlingham, Elsdon, Etal, Featherstone, Ford, Halton, Harbottle, Haughton, Langley, Lindisfarne, Mitford, Morpeth, Norham, Prudhoe Thirlwall, Twizell, Widdrington and warkworth +( Rothley which is a folly)