Yep I would swap the fuses around first and see if the indicators comes on and something else goes off then it will be fuse.
Do the hazard lights work? Do the windscreen wipers work as the wipers are running off the same fuse.
Mind you still check the fuses as or swap them around as the first option.
If not a fuse :cry:
It is not uncommon for Land Rovers to have bad earths due to corrosion.
There could be 2 flasher units, hence I asked if the hazards are working, if not one. The if you have to get behind the dash, be careful screwing it back in as some bright spark (pun intended) designed the main loom so that it runs in the channel behind the dash. The dash screws work against the loom and at that point there is no fused protection so a screw in the loom results in the loom melting, smoke, fire, etc etc.
Hopefully its a fuse. One of those 24v electrical check pens are very useful at this point.