Hello, my name is ***** ***** it is my pleasure to assist you with your question today.
I am afraid you have no rights to challenge their decision in the circumstances. An employer has no legal obligation to change their arrangements to accommodate your unavailability for a specific date and if you cannot make the date they have offered then they can remove you from the selection process. It is in no way illegal to do so. It may be immoral but that does not make it unlawful.
I'm sorry if this is not necessarily the answer you wanted to hear but I hope you understand I have a duty to be honest and explain the law as it actually stands and sometimes this does unfortunately mean delivering bad news from time to time. Please let me know if you need me to clarify anything.
No, your answer is as I suspected, I just needed to be certain thanks for your prompt response
you are welcome, all the best