right, a few myths are abounding here.
If your fed from a TNC-S system, then your minimum main earth is a 10mm, and this is to satisfy the bonding requirements of table 54.8 of BS7671.
with a TT system , you earthing copnductor should be sized to the lowest posssible resistance of your earth rod. The resistance of an earth rod is called Ra. Howveer your must also comply with table 54.1, which says that if your cable mechanically protected, then the min size is 2.5mm2, and if your cable is not mechanically protected, then the min size is 16mm.
On a TN system, and this method can also be used to size the earh to an earth rod, you need to use the adiabatic equation, or table 54.7 of BS7671.
the adiabatic is S= (square root(i2t))/k
i is the current that will flow in the conductor in an earth fault. This can be calculated from Uo/Ze, or your measured PEFC can be used.
2= squared (cant get the symbols on here)
t is the time taken for the protective device to tripwith the current above. this is found by looking at the time/current curves either from BS7671, or manufacturers info.
k is a factor that is listed in BS7671.
The adiabatic is the most economical way of sizing earthing, and circuit protective conductors.
Read chapter 543 onwards in the BS7671, page 160 onwards.