I had the same problem a couple of weeks back and freed mine using a socket on the nut.

Took the whole unit off the car, but you might be able to get a socket on without doing this.

I also had to buy a 22mm socket, as my set didn't go that high, but it was still cheaper than a new alternator.

I think Halfords quoted me

£160 for a new one, but I can't remember for sure.

Might be worth a try.
