I'd say if you want a break, take a break! Its your body not his!
But personally I'd find it harder to take a 10 min break and go back to it, you break the momentum and it takes quite a bit of effort to get yourself back to where you were before. But thats just me, it could be something you find easy to do!
It could also be though that your personal trainer has booked you in for 1 hour, not 1 hour 10 mins which means he is getting 10 mins unpaid and may well have back to back clients that he may be late running to as a result. Always ask first and maybe if he needs it, add 1/6 of the fee onto the session (multiply the session fee by 1.17).