B.C. and Trev are right.
Battery is storage for charge which is restored by alternator. When I had this problem (car charges enough, until lights are required), I carried a second battery... until swapping them in the dark by the side of the road felt stupid enough.
I removed the alt (gruntish task) and had it serviced by a starter/alternator shop.
Remember, you don't need a "new" alternator, any more than you need a new "car".
The alt is a system of serviceable components; I've posted elsewhere about the scam of a "new" alternator - they take yours, replace the bad part, clean it up (irrelevant to performance) and sell it as "new" - and they charge you full pop for a "new to you and clean" one.
Good luck.
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__Stef -- 81 DL wagon B21A SU carb M46 315555km