Are you coming from the outside water meter into the house i.e. renewing the communication pipe. Then its blue MDPE pipe, and change over in the Kitchen.
I would look up the Water Regulations if I where you or at least a guide to them.
If you don't do it right the customer will be one unhappy person. And some Water companies can be a bit "narky" over installations that are not done right. After all they would probably like the work themselves. You get it wrong and they may charge a fortune to put it right. But if you can show you have followed the Regs they can't do anything about it.
You can use plastic in the stack, but you have got to remember the weight of the cast iron stack will be forcing down onto it and the plastic will want to expand and move about a lot more than the cast iron will. But if you have no choice. Make sure you allow for expansion and the cast is firmly fixed all the way up. In my experience cast always settles down to the bottom regardless of how well you fix it higher up, its just so heavy.
Why not put a cast iron branch in instead.
But if your going from cast iron to plastic with all plastic higher up the stack, that is far easier, just cut the cast and get one of a variety of cast to pvc adapters, depending on which one you want.
May I also draw your attention to the fire aspects of soil stacks. They usually put cast iron in if there is a fire risk. When the stack is empty it can act like a chimney if its pvc and burns through. This may mean putting a fire check boxing in around a plastic stack. And don't forget sound insulation as well.
Also the stack may need fire stopping between floors.
Have a look at the Building Regs for room change of use if its a complete new bathroom. The house structure or joist spacing may not be strong enough. They may have to contact the council building control officer. And ventilation may need up rating as well as electrics.