1.5mm² or even 1mm² (which should only be used for lights) are more than adequate for a 2kw load.You could actually wire up a 3kw immersion heater in 1.5mm².
Yup, even in it's worst rated application 1mm2 t&e can take up to 10 odd amps if I remember rightly. Adding to that I'm sure a lot of domestic light switches you get are rated @ 10A too these days. Wouldn't be the recommended approach though TBH.
One for the leccy guys I reckon .... @EFLImpudence ?