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Can you tell me why you don't pay NIC please. Are you over the age at which you stop paying?
Strictly, your employer could make an amendment under the Real Time Information rules for PAYE to have your Class 1 NI deduction refunded. However, if they won't do that all you can do is to write to the address here explaining your situation and asking for a repayment of the NIC incorrectly deducted and giving them all the information asked for in the notes. Keep a copy of your P60 and the letter and chase them up on the phone after 4 weeks.
I hope this helps but let me know if you have any further questions.