As with all employment issues the answer to this will depend on what is written in your contract.
Employees generally have the right to be paid for work done or when they have presented themselves as willing and able to work during their normal working hours but you have prevented them from doing so.
The general right can be set aside if you have terms within your contract that give you some flexibility. What hours, if any, does your contract guarantee your Saturday assistant? Is she entitled to a minimum number of hours each Saturday or are her hours dependent on the rota and the needs of the business?
If you only have to pay her if she is on the rota then you have an argument to say that the rota was changed and she was not needed therefore there is no entitlement to pay. If your contract has no guaranteed hours, what is known as a “zero hours” contract, then your employee is only entitled to be paid for work actually done. As she didn’t work she would not be entitled to pay.
Do your contracts refer to any rights you have to reduce hours in accordance with business need? Do you have the ability to place people on lay off or short time working? Is there a right within your contract to require employees to take holiday in the event of an unexpected closure? If you have these options within your contract then you may be able to justify not paying or paying a reduced rate.
If you can enforce holiday then you will still have to pay this employee but it will come out of her overall holiday entitlement. Ultimately, though, unless you have an option within the contract that allows you to vary the hours or temporarily lay employees off without pay then your employee is correct. If her contract guarantees her a set number of hours on a Saturday then, as she was willing to work them but you prevented her from doing so, she would still be entitled to pay for those hours.