Could be lots of things.
Switch, break or miss-connection in the pipes or wires. Relay, if there is one or two?
First thing i would check, from experience on my Disco 2 is the connection at the back of the nearside of the bonnet as that is where my pipes came apart.
Fishtank pipe and connectors work fine.
EDIT
Just realised you meant headlamp washer not screenwasher so you can scrub some of what I said.
You are aware that it only comes on under certian circumstances, like the lights have to be on and the wipers on too? And that it will only work the once on a push it won't come on a second time.
(Can't remember the exact sequence but it doesn't come on every time you push the general washer switch.)
There is an awkward connection in the pipe behind the bumper and you may have to take the fog light out to get at it.
Just a question of working your way through it. Best to make sure at least one side is working so you can narrow things down.