Your employee has handed in their notice.  Apart from planning if and how you are going to replace them you will need to calculate how much pay they are due.

Calculating Leaving PayBasic Pay

How much will they be due for the pay period?  If they work monthly but finish part way through the month the pay they are due will need to be calculated.

Holiday Pay

Are they owed any holiday?  Or have they taken too much holiday for the proportion of the holiday year they have worked.  Holiday pay needs to be calculated based on the days they work each week and the number of weeks they have worked during the holiday year, not forgetting the bank holidays which are also included in the calculation.

Calculating holiday pay due can be very complex if an employee works variable hours and days each week.

If an employee has taken more holiday than they are due you can deduct it from their final pay.

Absence

Has the employee had any absences during the current or previous pay period which need to be deducted from their final pay?  If they refuse to work their notice period or have any other unexplained absence you are not required to pay them.

Other Deductions

Are there any other deductions that need to be made from the employee's final pay?  For example if you have made them a temporary loan which has not been repaid or for equipment that has been damaged or not returned.  Ensure that any deduction from their pay is lawful as set out in their contract of employment.  This is likely to be a deduction from their net pay and therefore will not affect their tax and national insurance.

Week in Hand

Some weekly paid employees are paid at the end of the second week they start work.  If this is the case with your weekly paid employees you must pay them the additional week of pay which is due to them with their final pay.

Finally

Every employee is entitled to a P45 and must be sent one when their final pay has been calculated.  Final pay will usually be calculated at the same time as the normal weekly or monthly salary and leavers cannot expect to receive their pay earlier than normal.  HMRC rules are that pay information is submitted to them on the same day or before an employee receives their pay.  

Ensure you get the calculations correct before submitting the final pay information to HMRC or to your employee as it is not straightforward making a correction afterwards.