I had a look, and think it is currently Sara Squire (the title seems to be Head of HR of the Royal Household) who is ex-Home Office and before that Royal HouseholdIf true they will have brought in an HR consultant or one of the law firms. The lady unfortunately does not have the experience for this and it’s not uncommon if a firm has a serious issue (especially if it involves senior people) to have a lawyer come in and handle the investigation. (I am in this industry so can comment)
Before that, the Head HR was Samantha Carruthers. Ex Deloittes, De Beers and Lazard, so looked experienced enough to cope with a mad Duchess to me.