His father was James Neilson, an Ironmaster and second cousin of Walter Montgomerie Neilson and his mother was Jane Thomson, daughter of George Thomson, the famous Glasgow shipbuilder. He attended Merchiston Castle School and was captain of the rugby and cricket sides and School Prefect. He represented Scotland at rugby while still attending Merchiston and then left to go to Clare College, Cambridge, where he also played rugby for the university before graduating BA in 1894.
Three of William's brothers, George Thomson Neilson, Walter Gordon Neilson and Robert Thomson Neilson also played international rugby for Scotland. George and Robert were also Presidents of the SRU. The four brothers never got to play together, although on at least five occasions, various pairings played on the same team.
In 1891, he made his debut, along with his brother George in the game against Wales. One of the four Neilson brothers played in each of the twenty five matches between Willie and George's debut in 1891, until 1899, when Robert had to withdraw from the Calcutta Cup line-up after breaking his nose.
Neilson became President of the Scottish Rugby Union in 1905.
- Bath, Richard (ed.) The Scotland Rugby Miscellany (Vision Sports Publishing Ltd, 2007 ISBN 1-905326-24-6)
- Thorburn, Sandy The History of Scottish Rugby
- Bath, p137
- "Neilson, Wiliam (NL891W)". A Cambridge Alumni Database. University of Cambridge.
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