It might make sense to bang some earth rods in as recommended by 411.4.2 anyway
From past experience of troubleshooting supply issues, one of the common things I come across is the just bang an earth rod in and all will be fine problem
There always seems to be a total lack of understanding and education these days when it comes to installing earth rods / earthing systems and testing them. Even some of the "specialist" lightning conductor companies seem to be lacking having recently looked at the work of one on a local church who couldn't even test the LPS properly and when it was pointed out to them by the church warden they sent out their compliance / training manager who agreed with my findings and mentioned to the church warden that he needed to go and amend the company training manual, a few years ago this company added an extra earth rod to the LPS without any consideration to it's siting in relation to the existing rods and earth mats
... with earth electrodes at the customer premises to support the T-N-CS system rather than converting it to T-T ... whether it will be possible to get an earth impedance value within the limits of table 54 I don't know ...
The problem with "supporting" the TN-C-S system is it can hide a failure of the PEN and as I and a mate of mine who is also an electrician have found the property can become the earthing point and neutral for a number of properties connected to that DNO supply line which then raises the issue of neutral currents flowing through the property with the earth rod from other co-located installations / properties
as I said, it is sand around here ... I suspect in summer when it dry as a nun's chuff may prove problematic!
If the ground is sand it is unusual to have a TN-C-S supply for the reason you mention, one of the DNO's local to me won't allow TN-C-S supplies in certain parts of their patch because of the ground being too sandy
The installation of earth rods / mats / discs / systems is IMO a subject all on it's own and with rods the assumption that a 4ft rod is all that is needed for an installation to be earthed is in a lot of cases IMO a demonstration of ignorance and the acceptance of some of the impedances that some find acceptable without taking into account the ground conditions at the time can in a lot of cases increase due to the ground drying especially during the summer months
When installing earth rods I generally take more rods than I think I need and always use the extendable type if I can get 8 or 12ft of rod down then I'm likely to get a low impedance if it is likely to need more than one rod I usually stick to 8ft so it is easier to properly co-locate the multiple rods
The problem with BS7671 there is no retest period suggested for earth rods or installations with earth rods and the maximum impedance values make no mention of possible seasonal changes of the measured values whereas BS62305 for LPS suggests an 11 month retest period to take account of the differing ground conditions
Guidance note 8 makes interesting reading