Is there anyway to change the interview date?

I'm an international student being interviewed at Cambridge, King's College. My interview is on Dec 10th but our Christmas hols start on the 18th and traditionally two weeks before hols we have everything due and the week before hols is much more relaxed. It would be much easier from a missing-school-days perspective if my interview was on any day from the 12th-15th of December instead.

Is there any way to request a change of interview date?

a friend of mine was unable to change hers (Homerton) for far more severe reasons- she had an exam clash on the day and is having to persuade her teacher to move the exam for the entire year. It sounds unlikely, no harm in asking though.

The only way to request a change is to contact the college and request a change.
It's not very easy for them to change, though, as the days your interviewers conduct interviews are fixed quite a while ago so that it won't crash with their other commitment/schedule.
You can try, but don't put your hope too high.