had incorrect NI number for years, all tax contributions paid towards incorrect one

First employer provided HMRC with an incorrect NI number which has been used for the last 5/6 years without me realising, I have now provided my current employer with the correct NI number which has been updated on my most recent payslip. However, all my NI and Tax contributions have been atributed to the incorrect NI number, how do I go about getting these assigned to the correct one?

Hi,
To enable HMRC to update your records using the correct National Insurance number, please write to us at the following address:
Individual Caseworker
PT Operations North East England
HM Revenue & Customs
BX9 1AN
Please provide the following information in your letter:
•    your employers name and address
•    the employers PAYE reference number, if known
•    the date you started your employment with that employer
•    the correct and incorrect National Insurance number
•    enclose copies of payslips or P60s for the relevant periods
Thank you