Call Land Rover North America and explain the situation. I have a feeling that the sale of LR to Tata came with some stipulations about out of warranty repairs. In addition, if it weren't for repair work at the dealerships, LRNA would surely see some of it's dealers go belly up. My '05 LR3 HSE is over 13,000 miles out of warranty and the dealer is replacing a cracked dash pad, no haggling!
Are you the original owner? Do you have all (or most) of your service work done at the dealer you bought from? Have you ever bought any accessories from their parts department? Are you a repeat customer? I can say yes to all of the above and my dealer has provided exemplary service, like the above mentioned dash replacement.
I have never bought an extended warranty and I'll keep this truck until monthly repair bills exceed the payment on a new one. Within another year or so aftermarket vendors will begin stocking all of the normal repair parts. You can buy a new transfer case online for a Discovery II, no doubt they will be available for LR3's soon.
Your T-case shouldn't have conked out so soon, follow-up with LRNA, be prepared to maybe pay the labor and resign yourself to having had some bad luck on this one item. All in all this is a very well built and engineered truck.