You should be consulting your HR department, not us.
I have worked in public service previously and it was normal practice to expect people to use up their annual leave during notice period, otherwise they have to to be paid for it after they’ve left, which is a cost to the department.
If you work in a department where leave usually needs to be arranged months in advance and it’s difficult to accommodate, I would thin it reasonable to ask, but not demand, that the person doesn’t take the annual leave.
The key thing to remember here, is that when a person gets a new job, they will be asked what their current notice period is. If they say 4 weeks (as that is what is in the staff handbook), then their start date may be agreed on that basis. So…if they aren’t allowed to take their annual leave, that doesn’t carry over to the new employer…meaning that the person might get the equivilant of an extra week’s pay that year….but they won’t have had the minimum statutory annual leave allowance accord the whole year and both employments. So if having to be paid for the week’s leave rather than take it within the employment….you are effectively making the notice period 5 weeks instead of 4, because really they should then I have a week’s gap to ensure they have that time off…but…that probably needs to be communicated as an expectation when you employ the person, not when they’ve already handed in their notice. There is also the issue that the employee may not be happy about that becuase they may end up needing to pay a voluntary NI contribution to cover any week that they aren’t officially employed anywhere…to avoid that gap causing them to miss out on whole year’s stamp.
You say being short-staffed is an issue, but what happens in week 5 once this person has left? Do you already have a replacement lined up…or will you also be short staffed then? If so, all you are doing is having an extra week of a problem that is going to impact anyway.
In a large organisation such as the NHS, it shouldn’t be down to the individual employee to have to do something unusual such as not take their annual leave, just becuase management haven’t got plans in place to cover. If someone was off sick, it would need to be covered, this isn’t any different.