Where has my reasoning gone wrong? If it's true that the specified supply tolerances relate to the on-load situation, the only possible weakness I can think of is my assumption that the impedence resulting in a supply-side voltage drop (with a TN-C-S supply) will essentially be equal to Ze
Nothing wrong with it, however the other items to consider are:
a. When installing large additional loads such as electric showers and storage heaters, the electricity supplier / DNO is supposed to be notified in advance so that they can confirm additional capacity is available.
If people don't, and the voltage sags all over the place after installing that 20kW pottery kiln in the garden shed, the blame is with those who installed it.
b. Where a single transformer supplies a number of properties, such as in most urban areas, the output voltage will continually be adjusted to accommodate the varying loads, so the volt drop issue is mitigated.
c. In rural areas where the supply is provided from a substantial distance away, the method appears to be to ensure the voltage with no load is as high as possible. (In most of the rural properties I have been to, the voltage is 245-250)
For the original question, if the lights have always dimmed when using the shower, probably nothing wrong.
If this dimming effect has recently appeared or got worse, there is probably a fault somewhere.