The answer, as it is in many cases, is …it all depends …
in this case on their reason for not working their notice.
If their contract of employment states that they must work out their notice period, if they fail to do so, they are in effect, in breach of that contract. And unless there are exceptional circumstances you, as the employer, do not have a duty to pay for any part of the notice period not worked.
However, if the reason for the employee resignation, was a breach of their contract of employment by the employer, the employee would be within their rights to leave without notice. However, as the employer, you are not under obligation to pay for the period of notice not worked.
Of course the employee can take the employer to an employment tribunal in these circumstances.
However, should the staff member not work out their full notice due to agreed absence on holiday, then they would be entitled to their normal pay during the notice period. Again, if the employee could not work during the notice period because they were off sick, they would be entitled to be paid statutory or contractual sick pay.
We hope this information is helpful,
The Graham Agency, keeping you informed.