UKPassats

Hi there, my first post. Having completed just over 337,000 miles I can't expect things not to go wrong on the odd occasion I suppose. However, my battery light has been coming on, on my dash with the "Alternator Workshop" displayed as well. On revviing the engine, the light goes off and stays off, allowing me to continue my journey. However it comes on again when I restart the engine. I have the car booked into my local garage and they tell me I will probably need a new Alternator, whilst they do the 340k service. Not that I begrudge buying a new alternator, but is the problem likely to be something less expensive. How much will a new Alternator cost?