For an alternator to begin working it requires a small supply of current called the exciter current. This comes from the battery, through the warning lamp in your dash (which illuminates and acts as a resistor) to the alternator via the thin wire.
When the alternator starts producing current the lamp in your dash will go out. This is because it now has voltage both sides of it so no flow of electricity so no illumination.
So I sounds like that your new alternator is not receiving it's exciter current. You have proved that the lamp hasn't blown so you must have a wiring issue at the alternator or your new alternator is faulty.
Maybe you could take it back to the dealer and whitness his alledged test.
By the way. The SAD landrover club has a laning day very close to you on Saturday. If you're not a member you can join on the day. Go to sadlrc.co.uk for details.
Cheers, Vince.