I will also have to change the lighting a little as the existing bathroom
light is on a pull switch, but the toilet light is on a normal switch which
will be inside the new bathroom. She wants only one central light and a
pull cord putting in the 'toilet side' and the other one removing. I have
the capabilities to do this but can I, with this new Part P regulation?

Of course you _can_ do it, but according to the govt you now _may_ not without involving building
control.