A farmer has a range of options for removing waste dumped illegally on his farmland. If the waste is posing an immediate threat to human health or the environment, he should contact the Environment Agency for advice. If the waste is of a non-hazardous nature, he must either remove the waste himself to a registered disposal site or contract a registered waste carrier to remove it for him. In both instances he should contact his local authority who may be able to offer support and advice. The exact cost of removal would depend on the nature and volume of waste deposited.
I have recently corresponded or discussed this issue with a number of farming and other landowner organisations.