Is it OK to have data lines and AC in the same multicore cable?
Operator safety and risks due to insulation failure are the primary concerns to address before even delving into the electronic side of the question. 

Keeping the above aside, the answer would depend on the current passing through the power cables. 

If the amount of current is large enough, the resultant electromagnetic interference on the other cables in the core would have severe detrimental effect. 

This is easiest to visualize if you consider the way a clamp-type current meter operates - a signal is induced in the clamp's coil proportionate to the current flowing through the cable under test. 

For moderate power supply currents, there exist special-purpose multicore cables specifically for the purpose described, such as Ambicore Cable:



Note that such cables have a separate insulation for the power conductors as a group, and that the signal conductors are typically shielded to protect signal integrity.