What would happen to the workload if you and your colleague said no? What would be the impact of your department being shut for a period of time? Would anyone suffer (I'm thinking care work or the like).
An employer can cancel previously approved leave provided they give adequate notice (the same notice as the length of the leave, so if you book 2 days they must give 2 days notice) and provided this does not prevent the employee taking the full statutory minimum leave for the year. So yes, she can do this. However, if there is no clear business reason and you suffer a financial loss as a result (e.g. because you've booked a holiday which you now have to cancel) you may be able to argue this is constructive dismissal unless they provide adequate compensation.
Putting aside the legalities, approving leave requests then arranging your own holiday to coincide with those requests and cancelling the employee's holiday is very poor management. "I've decided to take my holiday then" is not a good business reason for cancelling employee leave. I would refer this to your manager's manager or to HR.
Is there a policy on annual leave where you work OP? Does it say anything about cancellation of holiday already agreed?
It’s perfectly lawful if the correct notice has been given but it’s appalling management, and most places I know of where holiday gets cancelled there is a policy around what circumstances this might happen and frequently compensation for losses incurred.
They can cancel but must give the same notice of cancellation as the length of the leave booked, so 1 week if you have booked a weeks leave. I’ve had it happen to me and I was fuming. For me it was part of being bullied by my line manager.