I have a relation with a similar arrangement, i wrote to London Electricity (who is the supplier) who after a couple of months wrote back saying they would fit a TNC-S earth for £60, if I provided them with an electricians test and inspection certificate to show the installation was safe.
I am quibbling over the need for the test certificate, since it is not a new or changed supply, only an improved earth. Oddly enough the service head is only a few years old, a new plastic head was fitted to replace the old cast-iron one, but the earth was not upgraded at that time, the old pipe clamp was left in place.
The accompanying documents show that London Electricity (EDF) do the "supply" including changes to connections even if another company does the "metering" and you are billed by a different company; because EDF owns the networks, from the days when London Electricity was the monopoly Regional Electricity Company for London.
In your case you can write to your supplier (quote your account no) because you are their customer, and it is their responsibility to deal with whoever does the metering and distribution.