Hypothetical question?

What would you advise (any employment law experts out there or anyone with a view?) 

Person in a managerial position, attends work on daily basis, has not had a day sick since 2006 when a genuine bout of Flu kept them off work for one week. Person then (late 2014) discusses with Line manager about the possibility of a month off to tour a country, Line manager in agreement that it is a lovely prospect as indeed line manager is going to re-locate in retirement.

several weeks later, line mananger then comes to reportee to say they are NOT permitted to take said month (although 3 weeks can be booked without line managers consent). Reportee asks why and line manager says that because they, the reportee are the only consistent member of management who will do as bid (in the usual absence of their colleague; they are part time) and the reportee covers for their inadequacy,. ....Yes allegedly these were the actual words used.

the reportee states that this is not their problem rather, it is the line manager. That despite protestations from their line manager, the time off should be granted. The reportee is limited to time off due to the inadequacy of the colleagues they work with.

on a final note, the reportee is female (with a male manager) and the part timers are male (I say this before pre-concieved ideas of female managers and staff kick in).