"Falling down water"
Thanks for the response, Dave. The info you provided was well in the ballpark of what I was looking for. After making my post earlier, I googled "Railway Telegraph Pub" and saw quite a few listed. I figured then it might turn out to be a common sign with no real significance. What I'm actually hoping for is someone to say, "I remember seeing that sign!" That would be cool, and maybe even give some information of the exact location of the pub where it used to hang. Fat chance, I know, but there's always a possibility with some of the British railfans that post here.
I asked my client if he was going to keep it or get rid of it, and he said probably get rid of it. I'd love to have it and with your info above, it gives me a better idea of what I could offer him if he were willing to sell it to me.
Thanks!