Did customers have a choice of different companies to take on certain routes (e.g. London to Edinburgh)? Did this competition lead to lower prices? Did some companies become overly dominant in the market?
I thought about this whilst on a packed journey on the East coast recently and was wondering if there had ever been stiff competition in rail.
Yes on many routes there was fierce competition, on price, quality and speed. For your example of London to Edinburgh in 1913 you would have the choice of the east coast which would be trains operated jointly by the Great Northern to York, North eastern to Newcastle and North British to Edinburgh. By the West Coast London North Western to Carlisle and Caledonian to Edinburgh, and additionally the Midland London to Carlisle via the settle and Carlisle and the Glasgow And SouthWestern. Each offered different levels of comfort( the Midland as the slowest route was probably the most comfortable certainly for third class passenger) including dining and sleeping carriages.
Did it lead to lower prices ? The third class fare at this time was still set at 1d ( a penny) a mile by the government. But there was price competition in first class.
On some routes such as Plymouth to London competing companies agreed to share revenues. In this case after the companies had been speeding services up to try and gain market share, which had led to a disastrous crash at Salisbury. Services were slowed down, racing ended and revenues shared between the Great Western and the London South Western.