End of year tax code change not updated by employer

My tax code changed early March as my travel expenses were updated. My employer didn't change it in time and subsequently I will have overpaid income tax by £500. Do I need to do anything to facilitate a quick refund - clearly I won't be getting it back in my month 12 payslip as that has already been paid.

Hi

If you are in Self Assessment any refund due will be calculated when you  submit your tax return. If not in Self Assessment HMRC will review the tax year once your PAYe income details are received.
If overpaid a calculation will be issued to you. 

Thank you