An overpayment letter is a formal request to repay a debt owed to the Medicare Trust Fund. Payment is due upon receipt of the notice. Send the payment with a copy of the overpayment letter received or request an immediate offset.
The DWP can agree to waiver (write off) the overpayment. However this will usually only be done in exceptional circumstances where recovery action will result in severe welfare issues for you or your family. The DWP will also look into the circumstances of the overpayment.
You should only be required to repay the amount of overpayment that you actually received. It is down to your employer to make arrangements for the recovery of tax and National Insurance.