If the battery light doesn't go out when engine running, you can be 95% certain its a faulty alternator. To be 99.99% sure, take it to an auto electrician who can do a 'spin test' of the alternator, ie he tests it off the vehicle. He'll probably also be able to rebuild it at a lower cost than a replacement alternator. By all means, you could buy one off a scrappy etc, but there's no guarantee of its longevity.
A check of the relevant fuse(s) is always worth doing anyway, since its quick and easy.
Hi Paul
Thanks for the replies...
I think we're 99% certain that the altenator is indeed kaput. The fuses have all been checked, and whilst one did happen to be blown, it wasn't for the alternator in any case, and after replacement, made no difference.
The key problem is:
LR Main Dealer - £400 for a Denso OEM part
LR Breaker in Scotland - £35 (+postage of £10) - bought with the protection of Paypal in case its a duffer when it gets here.
The warranty on the new part is only 1 year - I'd have to get through more than 11 used ones to break even! It's a no brainer for me....