Andy,
A domestic ring main is 2.5mm that is correctbut it is a ring main, The clue is in the name
Long cable runs like the OP enquired about is an extension, and not part of the ring main.
Any fool knows that the longer the cable run, the higher the resistance. However, when a long run is needed, you need to specify the correct size cable. Your analogy of the kettle and roster has many holes.
Check the power rating of both the kettle and toaster. I bet your toaster draws a much lower current (thats amps) than your kettle. Both the toaster and kettle use separate cables, and whilst they are plugged into the same double socket, the cabling behind is a ring main.
So, the 2.5mm ring main has an easy theory behind it, resistors in parallel so, total resistance=(1/R1)+(1/R2)+(.....) Therefore, in a ring main, the total resistance in the ringmain from mcb to socket is less than lowest resistance of one of its component parts.
The kettle elements the OP asked about are to be run at a distance from the ringmain on a single cable. 10 metres does not sound much, but in terms of maximum voltage drop (and therefore current rise) is significant, especially when you factor in the load demand.
Bigger cables have less resistance, and therefore, the losses to the cable are lessened (back to the ring main - there is 5mm CSA cable to your socket) so, to reaffirm, I still advise 2.5 mm cable, not to be funny, or to make someone pay more than they should, but to be safe, and legal with regard to the electrical regs in this country.