I'm looking for a landline phone (not necessarily cordless) which runs on Android and gives me the associated control, customisability, and for a bonus, market access. Does such a thing exist?
Apparently Yes. The Archos Smart Home Phone is an Android Phone priced at £130 in the UK:
Although the reviews on Amazon UK arent very good:
Binatone iHome Phone iDect with DECT and Android Technology
Currently unavailable (maybe its that good)
The iDECT iHomephone has Android.
I do not know whether or not it comes with Google Play however.
Motorola also has a device similar to the Archos Simon mentions, though they don't seem to be available for sale yet, despite clearing FCC approval back in April.
Binatone also offers such devices, though it appears to only be available in Europe
There's also Android-based VOIP units, like the Panasonic KX-UT670, though I imagine that isn't what you're looking for.