While this thread is talking about Kelso I give you the following.
I came across the name some time ago but knew nothing about the company. As I was at The National Archive yesterday, seeking information on the real Waverley Route, I looked it up.
The Carlisle & Berwick Junction Railway - (With a Branch to Hawick).
Incorporated Oct 3 1845.
To make a line of railway from the town of Carlisle in the county of Cumberland to Kelso in the country of Scotland, there to join the Newcastle & Berwick Railway at that place.
This was but one of several schemes from around that time.
Bernard