Can I get planning permission for a house in my field?

Generally this would be considered a development in the open countryside and is likely to be resisted by the planning department. If the proposed development could be considered to be rounding off or infill then you may have a better chance. You should also check to see whether your Parish has a Neighbourhood Development Plan, which may dictate where development is considered acceptable. If you have an existing barn or even a modern agricultural building there is scope within planning policy to convert it into a home.