Almera new alternator but still cutting out

[Leffemonster]

Now, I know very little about cars... My 2002 Almera 1.8 saloon cut out at the weekend. Nice man from the AA advised very low output from the alternator and possibly need for battery replacement. Local garage have fitted new alternator and advised me to take the car for a run, which I did last night. Car duly cut out again after about 10 miles on the M20 but restarted after a 5 min wait, then cut out again after about another 2 miles. Waited and restarted again, lasted almost 15 miles but then did it again. Got home and noticed near side front lamps blown as well.

Now, as I said I'm not mechanically minded, but from what I have read one of the main aims of alternator is to kick the car off and then provide charge back into the battery. If the battery is goosed, which may be the case, I don't understand why the car restarts after a short wait and then continues for a few miles. Surely if the battery is knackered then it's knackered?

Engine management light is on, so presume needs clearing with OBD scanner? Anyone any ideas what might be the issue, or is it just a case of a new battery? Spoke to a mate last night who suspects it might be dodgy coil packs (whatever they do...)

Any advice gratefully received.

Cheers, Nick