Given that the secondary battery doesn't really cause any issues if you disconnect it (other than disabling the stop start), then it makes me think it's far more likely the alternator itself is duff if it's bringing a not charging fault up.
I would also see if you can do a bit of research and see if you can source (a genuine) one from somewhere other than Jag themselves, as essentially they'll probably add about £200 just for the fun of it.
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