What does this give you for 'city'?
Keswick, a tiny town in Cumbria.
I tried some other geolocation sites while I was at it:
* maxmind's GeoIP2 demo says Wigton, Cumbria
* geoiplookip.net doesn't detect a city but its map also shows Cumbria
* ultratools shows Barnet, London
* geoiptool.com shows my actual location in southern Scotland, down to the correct first half of postcode (!)
Looks like I can't reliably detect the PPPoE exit point from the IP, then. Thanks for the idea though...