Slipping/knackered auxiliary drive belt. Alternator low output. (One diode failed, or brushes low?) Loose/dirty connection in the charging circuit.
If you have a reasonably accurate meter, you can measure the following voltages across the battery:
When it has been standing all night. When first started with no extra load. At idle with everything switched on. At fast idle with everything switched on.
You can either post the results here, or look online for what they should be.
Should it not be possible to carry out those tests, seek help. If an AA/ RAC member, they carry automated test equipment that is reliable. If you have 'Home Start' you could always suggest that it wouldn't start ;-)
Or cool when you need it! We had a hire car with the remote start option. It was very handy for reducing the cabin temperature to tolerable before entering it.
A friend of mine had the same fault: Cold weather, started up, left it running, came back to no charge and the belt snapped: Cause: frozen water pump meaning the belt slipped on the pulley till the belt heated up and dropped apart. Cure: add anti-freeze and renew belt. Also seen when the aircon pump seizes.
Unless they rushed it and only 1/2 filled a cell. No doubt it appeared full when they capped it, was 1/2 full when I got it home. They don't last 6 months after starting a few times like that.
We're talking about the country of free gas here. Don't be daft. ;-). Besides, would you really want your car windows opening when you're not close enough to apprehend a tea leaf?
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