Findmypast.co.uk have made available the Great Western Railway Shareholder Index, originally compiled by the Society of Genealogists. According to Findmypast the index doesn’t include every shareholder of the GWR, but amongst the 570,464 records it does include details of around "440,000 shareholders and related parties, such as executors and spouses."
The index was originally created by the Society of Genealogists and has now been linked to "full colour scanned images" of the original ledgers. The ledgers record the transfer of shares by means other than by simple sale.
Many of the records relate to a transfer of shares brought about by the death of a shareholder, so if you are lucky you might find details of the death and probate of the individual, along with the number of shares held and the new owner.
Perhaps not surprisingly it doesn’t look like any of my ancestors were shareholders of the GWR. A quick search of the collection’s index failed to find anyone who was even remotely connected to me, still it was worth checking.