My interpretation of the current regs. would also be that the 10mm is fine. If you are going to use an earth "spike" ( which may of course need more than one, depnding on soil resistance) then you would be advised to make it a TT system (with RCD) totally independent of the house earth. Remember also that if you choose this option you must dig down at least 600mm BEFORE you knock in the earth rods, to ensure a good connection. Otherwise stick to using one core and sheath of the SWA, remembering that if you have any extraneous metalwork in the summer house, e.g. pipes, these must be bonded as normal.
