I no many PhD positions are funded for 3-4 years but are there any fees the student has to pay to study for a PhD - like uni tuition fees?

typically, the uni fees are covered by the funding.
If you're not sure about it, just ask the person you are applying to. He/she should be able to tell you what is covered by the funding and what not.

Some PhDs are funded only partially, just given some amount a year. Then you have to pay tuition fees that always have to be paid and they can be from 3000 to 12000 pounds a year. But there are fully funded PhDs whose tuition fees are paid and plus they get 10-12k pounds a year for living expenses. That's in the UK.