Week 1 Month 1 National Insurance

After leaving employment and receiving my P45 in October, I was paid back pay to cover overtime and a pay rise owed from the preceding 2 months in November. This was paid by my local authority (I am a teacher) using Week 1 / Month 1 and in addition to 20% PAYE I also paid National Insurance, despite the fact that the payment was not for a week's worth of employment. How can I claim a refund for this?

Hi 
Thank you for your query about claiming a refund of National Insurance contributions.
The National Insurance contributions calculated by your employer may be correct and may have been correctly calculated on a weekly basis.  
Your first step would be to contact your ex-employer to ask them to check the amount of National Insurance that they have deducted is correct.
If any refund is due they may be able to process the refund for you (they can contact the employers helpline if they require assistance to do this).
If your ex-employer is unable to, or refuses to check the National Insurance deduction and process any possible refund, you can write to HMRC at the following address:
National Insurance Contributions and Employers Office
Payment Reconciliation
HM Revenue and Customs
BX9 1AN
Please enclose a copy of your final payslip with your letter and your reason for requesting a refund.
Thank you.