Might be the rubber latch switch has corroded.
Per the links below, corrosion of the contacts of the switch under the rubber thingy of the rear hatch button is common. The good news is that the switch can be purchased separately, (part number YUZ500020), and replaced without tearing apart the interior from the hatch door - that is, you can do it all from outside.
This is the link onto the disco3 forum re the D3 and the fix. It makes reference to the link following to the RRSport forum. The switch parts are the same for the LR3, the D3, and the RRS. The repair technique is similar - pry out the rubber bit and then snap in the new switch assembly. Some try to clean up the old switch contacts but ....
http://www.disco3.co.uk/forum/topic66951.html?highlight=YUZ500020
http://www.rrsport.co.uk/forum/topic17072.html
Prior to the repair, you can pretty much determine if this is the problem by using the emergency hatch open technique as explained in your owners manual. Basically it takes two people; one person to hold down both the lock and unlock buttons on the dash at the front for maybe 30 seconds until a click is heard. When the click noise happens at the rear, the second person manually lifts the upper hatch as holding of the two buttons only releases the catch, but does not actually open the upper hatch. The two front buttons must continue to be held down until the hatch is lifted.
If the emergency release process works, then the problem is merely that the rear hatch button is not working and hence should be replaced.
If you get the clicking but no release, then the problem is a broken cable inside the lower door. If so, then the following links.
http://www.disco3.co.uk/forum/topic27461.html
http://www.disco3.co.uk/forum/topic65601.html
http://www.disco3.co.uk/gallery/albums/userpics/22682/Tailgate_Actuator_DIY~0.pdf