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Hi, thanks for your enquiry.
I am afraid that as your use of the field had bee with the express consent of the deceased owner, you have not acquired any legal rights over the land, and all you have is an oral Licence agreement, meaning that you have the right to carry on using the land until the owner (or his next of kin) asks you to stop.
I know it sounds daft, but only if you had been using the land WITHOUT the consent of the owner for a period of 12 years or more would you have acquired any legal right to remain in possession of the land.
Therefore, the deceased owner's sons are within their rights to ask you to stop using the land immediately or suggest a written Licence agreement.
I am sorry this is not the answer you were looking for, but it sets out the legal position.