Could you please read below from the HMRC website and advise further?
PAYE90001 - Reconcile individual: underpayments: introduction
PAYE underpayments arise if the individual has not paid enough tax during the year. This could be because the tax code was reduced during the year or the wrong tax code was used.
Most PAYE underpayments can usually be included as a restriction in the tax code for the next complete year. However there are circumstances where this is not possible, for example, underpayments of £3000 or over (whether for one or more years) and / or underpayments of less than £3000 that, due to circumstances particular to the case, cannot be collected through the tax code (PAYE12080).
An underpayment of any amount that arises through the employer failing to deduct the correct amount of tax from earnings (perhaps by not using the correct code) must be recovered in the first instance from the employer. The underpayment may only be recovered from the individual if a PAYE direction is made centrally by either the PAYE Errors Unit or a PAYE Direction Unit. A PAYE direction effectively transfers liability for tax under-deducted from the employer to the employee. Further information on PAYE direction is available at PAYE90020.
Also HMRC Guidelines Employer Further Guide to PAYE and NICs - CWG2(2011) states on page 18:
"As a general rule, you as the employer have to pay
any underpayment of PAYE arising from a mistake
in deductions. However, a direction can be made
for your employee to pay an underpayment if we
are satisfied that you took reasonable care and that
the underpayment arose from an error made in good faith".
Are you able to comment further please?