He was born on 19 November 1855 in London, the son of Dr J W B Steggall of Charing Cross Hospital, a physician and surgeon, living at Queen Square in Bloomsbury.

[1] He attended the City of London School before entering Trinity College, Cambridge, where he graduated second wrangler in the Mathematical Tripos of 1878 and winning the Smith's Prize of that year.

In 1883 he was appointed as the Chair of Mathematics and Natural Philosophy (Physics) in the newly instituted University College at Dundee.

His proposers were Balfour Stewart, William Evans Hoyle, Patrick Geddes and Peter Guthrie Tait.

[7] Their only son, John William Abbot Steggall, was killed on 31 May 1916 serving on HMS Invincible on the first day of the Battle of Jutland.