Advice Please! On leaving my old job and starting my new one?

I have handed my notice in at my old employers who is being quite unreasonable about the possibility of changing a few hours because im starting my new job whilst in the 4 week notice period. However my new employer is also being unreasonable asking to cut the 4 week notice down to less, althought they new about this when i had my interview. They have both put me down to work the same shift, but not sure what to do?