Open with
Hi, I'm calling about my interview.
Then say
- It's Alex, booked for Wednesday at 10am.
- Something has come up and I can't make that time.
- Would it be possible to move it?
- Tell me what suits you and I'll work around it.
If they ask
- May I ask why?
- I have a commitment that day I can't move.
- We can't reschedule.
- Understood. I'll come at the original time.
- When are you free?
- Any day after 10am works for me.
Ending
Thank you for working around it.