2C 16mm SWA should be 1.15 mOhm/m for R1 and 3.7mOhm/m for R2, so R1+R2 ought to be around 0.49 ohms. as
@SJD says what you are seeing is a lot higher than realistically expected here so look for loose/corroded glands at the ends, or missing banjo+flying leads so it is depending on rusty/painted enclosures for the CPC.
If both ends are good and clean then it points to a more worrying aspect that it could be corroded armour underground somewhere, but that would usually take years to develop following puncture of the surrounding sheath. Also IR the cable on its own (both ends disconnected and wiped clean of any dust/damp), that might indicate water ingress somewhere if it looks low-ish.
More generally you won't get much of an improvement with an earth rod, often it is hard to get Ra below 50 ohm with most soils and that is not going to make a significant change to 2.4 ohms.
If after fixing it still is too high for the supply OCPD then fitting a delay RCD along with the MCB/fuse feeding it is another means of ensuring ADS times are mot and you still have a sporting chance of selectivity with end circuit RCD/RCBO at the annex CU.
You could use a rod and delay RCD if the armour is failing and cable otherwise OK, in effect making the annex a TT system with part of the sub-main on TN earthing (to the corroded segment) and the end of the system on TT using the rod at the annex. But you have to be able to meet ADS on the rod alone, hence the only realistic option is a 100mA or 300mA delay RCD as part of the supply protection.