I'm sure I read something on this before but had no luck searching. Something about a blue wire?

Anyway, Battery light is glowing slightly and illuminates when braking or using the windows.
Car recently had a new alternator and is reading 13.6 volts at the battery.

 

check your main earths, sounds like a corroded earth to me?

 

The wire is fine.

As said, it's most likely to be a bad ground, and you will probably find it will get brighter with load.

Martin

 

It does get brighter under load.
I will have a look at the earths at the weekend.

 

The blue wire goes from the battery light to the alternator and is what excites the charging circuit, if this is broken you will get no charge at all.
I would suspect either the live wires from alternator to battery (via starter) or the main earth's including the starter earth (biggest one on the car).

 

Put a jump lead from the engine block to the battery negative, see what happens then. If it is back to normal, I'd definitely say an earthing issue.

 

Cleaned up a few earths today and it's made a big difference.

Would it be worth cleaning up the lives on the starter alternator as well?

 

Certainly wouldn't hurt. Spray all the terminals in battery terminal spray after, you wont get any corrosion again.

 

I think the main live going to the starter motor was the culprit. It was a right rusty mess.