It is the responsibility of the employer (the council) to deduct PAYE and employee national insurance from their employees. Sometimes there will be additional deductions such as an Attachment Order or a Salary Sacrifice as well. 

These deductions are made from the employees gross pay and it is then the net pay which is paid to the employee. This can be found in the bottom right hand side of your payslip. 

It is then the responsibility of the employer (the council) to pay these deductions along with any employer national insurance directly to HMRC either monthly or quarterly, depending on the set up. The total liability due can be found at the bottom of the P30 which I issue you either monthly or quarterly, along with the payment details and reference to include when making payment to HMRC. 

An employee must not be paid their gross pay and pay tax or national insurance to HMRC themselves and an employee must not also make payments of PAYE and NI to HMRC directly (unless acting on behalf of the employer). 

Tax Refunds

If an employee is owed a tax refund, this appears on their payslip as a negative tax amount and will be added on to their net pay for the employer (the council) to pay directly to the employee. This refund must be paid by the employer and not claimed back by the employee from HMRC, if a tax code to action the refund has been issued. 

This refund will then come off any PAYE and national insurance liability the council may have within that month or quarter and if their is no further liability, a letter will be issued by HMRC after year end on how to claim this money back. 

This should not prevent the council from ensuring that they are paying their employee the tax refund. 

Further note, you will likely have employers national insurance which you did not have before this financial year, this will be included on the P30 and it a contribution from the council not a deduction from the employee which is why all liability must be paid together, by the council, to HMRC