I am also interested in the history of electrification. Out of all the possible ways of delivering power for rail traction three main systems were in UK use and competing in the period from the 1890s up to grouping.
Third rail (and 4 rail), at voltages in the 600v DC range. Adopted by many early systems, including LSWR, Liverpool Overhead, Tyneside electric (NER), LNWR Watford DC lines, Metropolitan Railway, and the L&Y around Liverpool and all London deep level underground lines, as well as a few others.
~6kV AC 25Hz OHL, pioneered by the LBSCR in South London from 1909 and the Midland Railway with their Lancaster – Heysham project which went live in 1908. The low frequency came about because series wound motors will work on AC, but 50Hz is not viable for constructing motors in the 100's HP range. There is quite a bit of information on the LBSCR system available in the Electric Railway Journal in the 1909 -1911 period. The LBSCR saw this system as a precursor to main line electrification to Brighton and beyond, but WW1 intervened and then grouping meant that the LSWR third rail system became the SR standard. I am not sure what the Midland longer term plans were.
The one which people tend to forget is the Shildon – Newport electrification completed right at the start of WW1, using 1500v DC OHL. Vincent Raven and the NER saw this as the test bed for ECML electrification in the NER area, and even went as far as constructing an express locomotive, No 13, later numbered EE1, just after WW1 which never actually ran as intended as grouping and the post WW1 financial situation stopped the plans for further electrification in the former NER territory. The 1500v DC system later became the standard, prior to 25kV 50Hz being practical, but apart from Woodhead, Manchester-Altrincham and Liverpool St Shenfield never really became established
Then there are the outliers:
1200v DC Bury Manchester by the L&Y and a short lived 3.5kV DC OHL test system from Bury to Holcombe Brook. The 1200v DC side contact is interesting, obviously less susceptible to ice and snow, and the higher voltage equates to lower losses. All other things being equal (same conductor rails and cables) for a given supplied power losses at 1200v are roughly a third of those at 630-650v. Did the LY see it as a possible longer distance system, over the Pennines. I believe 1200v was the highest voltage the BoT of the day would allow at ground level. It also used well proven technology.
I think the 3.5kV DC test bed came about because Dick Kerr & Co. in Preston were developing this system for export. Were the L&Y also considering this system for further 'main line' electrification.
Another outlier is of course Volks Railway in Brighton, starting off at 50v DC at opening in 1883, and then increasing to 160v DC a couple of years later when rebuilt.
Third rail really was the main system in the period from WW1 to WW2, it was simple to install, the technology was well understood. 1500V DC never really got going, by the time main line electrification was funded 25kV 50Hz AC was feasible and the better solution.
Interestingly the one major rail company which never dabbled in electrification was the GWR, I know there were plans for 3kV DC OHL in the SW, but these never really got beyond plans.
I think the most interesting what if is Vincent Raven, had he become CME of the LNER I suspect the electrification of the ECML would have happened, and the history of that line would be very different.
There were other systems tried overseas, various 3 phase configurations, with two overhead conductors and using the running rail as the 3rd phase. Otherwise up to the developments in 25kV 50Hz technology just about everywhere used either 3rd rail DC, DC OHL in the 1kV to 3kV range or low frequency high voltage OHL. Each system has advantages and disadvantages, but it needs to be born in mind that before the advent of power electronics there were a lot more compromises to be made when selecting a system.