Faced with an estimate like that I would start looking for a reasonable used axle (plenty of these vehicles being broken on ebay normally) and then swap it myself. Expect to pay around £300 for an axle? Make sure you tell the seller you will be bringing it straight back if it is no better than your existing axle (but not before you agree a price!)
Swapping the axle is fairly straightforward if not a little physical, I've done dozens on Jeeps and Landrovers and even faffing about fettling brakes and anything else you find while your at it it is an easy 1 day project for a reasonable DIY'er with a break for lunch.