Pretty common problem with the LR3s - it is likely a blocked sunroof drain. Here is some info from a TSB:
Technical Service Bulletin No.LA501-014
24 October 2005
Subject/Concern:
Discovery 3 (LA) - Possible Causes of Water Ingress into the Cabin
Models :
Discovery 3 / LR3 Vin range : 5A300394 Onwards
Markets :
All
Section :
501-01
Summary :
This bulletin has been issued for information only to aid technicians in identifying possible areas of water ingress into the cabin.
Should a customer express concern, and having located the point of water ingress, the appropriate remedial action should then be carried out.
Symptom
Water Ingress through headliner in proximity of roof opening panel. Sealed end valve of the roof opening panel drain tubes. This may affect any one of the four roof opening panel drain tubes on the vehicle.
Potential Root Cause
. Loose roof opening panel torx screws.
. Badly routed, kinked or twisted roof opening panel drain tubes.
. Incorrect lateral position of roof opening panel lateral alignment, causing the seal to leak. Note; This root cause will result in substantial water ingress.
Symptom
Water Ingress through headliner in proximity of roof opening panel, predominantly front right-hand side of roof opening panel although depending upon inclination of vehicle, or acceleration/deceleration, ingress may be evident at other points around the roof opening panel.
Potential Root Cause
Foam sound-deadening pad in right-hand side fender/wing air intake fouling/blocking the roof opening panel drain tube.
Good luck!
Rich