Cable sizes are selected according to:-
Earth loop impedance.
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.
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