Cable sizes are selected according to:-
Manufactures recommendations.
Earth loop impedance.
Volt drop.
Protection device size.
Environment i.e. insulation in walls.
Likely 1.5 mm sq will comply but until you have measured the earth loop impedance for example you will not know.
Since you will first need to inform LABC and they will want to either see your test results and/or test themselves with a bathroom there are no short cuts.
Likely getting an electrician who is a member of a scheme will be cheaper than DIY.
DIY how to tutorial projects and guides - Did you know we have a DIY Projects section? Well, if no, then we certainly do! Within this area of our site have literally hundreds of how-to guides and tutorials that cover a huge range of home improvement tasks. Each page also comes with pictures and a video to make completing those jobs even easier!