V40cc D3 starting / battery issue?

[JonnyA]

Hi
Our D3 (13 plate) appears to be reluctant to start on fairly frequent occasions. Its not that it doesn't start, but it may take several presses of the button to get it to fire up.
Also the start/stop system has stopped or rather is in active. In the DrivE menu it shows as being due to battery charging, even after quite a reasonable journey.
My suspicion is that the battery may be on its way out so not providing enough oomph for a quick start and therefore the S/S is deactivated.
Went out this morning - a good frost, car showing -3deg.
checked the battery voltages: opened bonnet 12.3v, ignition on 12.0-12.1 volts, engine running 15.2v (it started with no hesitation this morning) with all electrics on that I could turn on 13.2v, engine and ignition off 12.5v, ignition back on 12.0v, ignition off slowly recovered to 12.2v.

it strikes me that the battery voltage is a bit low and I am surprised that the cars basic ignition on (no select-able systems on) drops it noticeably. The charging system seems to putting out plenty and more than enough to deal with cars demands.

Am i thinking in the right direction?
(it had the rear door lock replaced a couple of weeks ago, the garage checked the error codes - the only current one related to the power steering module and was apparently unwilling to clear. They also put the battery on charge, they didn't say but that makes me think they too thought it low)