Let me preface this by admitting up front that I know virtually nothing about Land Rovers, but I have worked on a LOT of different kinds of cars in my lifetime.
From my reading it appears there's an common problem with the fan relay where it provides voltage but no current. Therefore it will appear to be working correctly on a voltmeter but since it's not providing any current, it won't turn the fan. Testing it appears to be fairly easy; you simply swap the front and rear relays since they're the same, and if it then starts working you've found the problem.
Relay R10 powers the rear fan and R16 runs the front fan. Here's the diagram that came with the post I found.
[image|3165571]
Here's what it looks like in the car.
[image|3165573]
Here's the full post on the Land Rover forums where the issue is being discussed.
[link|https://landroverforums.com/forum/lr3-28/front-blower-fixed-65098/|Front Blower--FIXED - Land Rover Forums - Land Rover Enthusiast Forum|new_window=true]
I would suggest you swap those two relays and let us know what happens.