Started the car yesterday evening to go home and the battery warning light stayed on. Turned it off and started again, no battery warning light.

Undertook the same journey today. No warning light getting there. Started car in evening and battery warning light was on. Multiple restarts and light still on. Drove down road 500 metres and pulled over. As I put the car in to Park the light went of and stayed off for the remainder of the journey.

Is this a failing alternator or just dubious electrics?

Be worth getting your alternator checked before you run down the battery.

Plugged in the IID tool this morning and the battery was at 11.7 volts. Once the engine was started, with no illuminated battery warning light, it was showing 14.0 volts.

Does that sound like an alternator on the way out or the battery?

Could be either, a battery at that voltage is a discharged battery for one of two reasons, it's not charging or it is discharging itself.
14.0 V is ok on a Td6 for charging from the alternator but your problem is the battery charge light seems to come on intermittently which suggest 14.0V isn't consistent, which in turn suggests the alternator is on its way out.
You could try charging the battery overnight and see what happens.
My money would be on a failing alternator but it could equally be both a failing alternator and a bad battery at the same time.
You really need to get it checked before you get stuck.

As above. Have you checked the alternator output when the warning light is showing? John
2008 Stornoway Grey 3.6 Tdv8 Vogue
2005 TD6 Java Black Vogue - Written off!!
GAP iiD BT
2003 Discovery TD5 Auto, Nanocom Evolution - gone to a new home!
MasseyFerguson 152 - No electronics!! - Sold

I had the same and upon striping the alternator apart found the brush gear worn to an extent where one of the carbon brushes was not making contact. Ordered some replacement brushes online and fitted them myself. Rebuilt and refitted and now has been ok for the past year + . Mine is a 52 plate TD6 with 167k on it.