Hi
If the incorrect date was submitted by the employer then they should submit the amended details online.
If your previous employer will not do this you can submit the letter they gave you with the correct details to HMRC at
HMRC,
Self Assessment & PAYE,
BX9 1AS
UK.
If you tax code is incorrect then you will need to contact HMRC to review.
You can contact HMRC at
Income Tax: general enquiries