Welcome aboard, what an interesting question!
I can only offer advice as an employer and from experience, versus being legally correct, but I tend to fined common sense can settle most issues. Few people genuinely want to go down the road of a tribunal.
The employees holiday entitlement will be written in black and white in their employment contract. As long as this conforms to the minimum legal entitlement, then I would put the responsibility of keeping track on holiday days on the employee. The company will obviously keep records, but this is primarily to manage resource as well as keeping track of employees entitlement.
If it was me, I would go in and have a 1-1 with her and explain your options, ie cancel 4 days, or if not possible, explain you are willing to allow authorised absence but it will be unpaid.
If she starts banging on about employee rights, then refer her to her contract and stated holiday entitlement. Depends how valuable an employee she is to you, and how she values her job. If she wants to start raising legal arguments, then that's hardly going to generate a friendly team atmosphere.
Plan B, if she's very belligerent and you think the situation is going south, then accept it's your cock up, put stricter holiday controls in place then manage her out of the company as soon as possible
If you are genuinely worried, the ACAS site is a good place to start: ACAS - Holidays