The Great Western was, as always, the exception that proved the rule. Except for the
Counties, all GWR locomotives were right-hand drive all the way up to the end. That was in fact the traditional side to put the driver, simply because it had always been done that way, copying traditional stagecoach practice, which copied charioteers (whose spears were in their right hands, so they sat on the right in case they met an enemy coming the other way). Signal-sighting and tolken-collection issues meant that most railways swapped over around the time of the Grouping. In fact, some A1s were built with the driving position on the right, but this was switched when they were rebuilt to A3s. Some passing stations with island platforms, on the West Highland for instance, used to see trains running wrong line to make tolken exchange easier.
Where British locomotives ran on foreign lines, places where trains run on the right such as Germany or the US, they never bothered to swap over. France, where many lines were British-built, copied us and ran on the left, but swapped their drivers over with domestic-built locos.
Meanwhile back on the GWR, the
Britannias were disliked by some crews because the driver was on the 'wrong' side. However, a combination of sitting in the wrong place, smoke deflectors and signals set up to be visible from the usual driver's side led to a number of what we now call SPADs and one serious accident at Milton, where the driver apparently misred a signal, took a crossover too fast and ended up rolling down an embankment. All WR
Britannias had their smoke deflector handrails removed to improve forward visibility after this.
http://en.wikipedia.org/wiki/Right-_and_left-hand_traffic#Trains