You can, and that is basically the whole point about the UK-style of T&E cabling having a smaller CPC, simply by:
- (a) checking the adiabatic limits
- (b) ensuring it is protected against mechanical damage and corrosion.
Although you can get 16mm T&E in the UK it is rare, typically the biggest you will see in (sort of) common use is 10mm for the likes of large showers or big cookers in a domestic situation.
So the reality is most domestic final circuit wiring in the UK has a reduced CPC and that is fine due to the I2t from MCBs and fuses (when the design is ensuring a disconnection time below 0.4s) satisfying the adiabatic check.
The "half phase size above 16mm" rule is a very basic choice if you are not in a position to validate the I2t that a fault could have. Typically by that size you might be looking at up to 5s disconnection times for a sub-main or main feed cable, and so quite high I2t (even at short times if it is a MCCB that is providing the over-current protection from a source with a very high PFC).
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For a typical earth rod you are quite right, no way are you going to roast even 2.5mm on a fault on a TT system, so going to 4mm or more would only be for mechanical strength I guess.
Where the UK has a higher earth bond conductor requirement is for TN-C-S where it might be bonding to a shared water pipe or gas pipe, etc, and in a PME fault case could be seeing high tens (or possibly hundred-ish) of amps flowing as all of the unbalanced neutral currents in that section try to use whatever route the can get home by.