Born 5 March 1876, Norton, East Riding of Yorkshire, England, Iremonger played 334 first-class matches for Nottinghamshire between 1899 and 1914, scoring 16,622 runs at 35.06 and taking 619 wickets with his right-arm medium-pace at 22.98.

It was though he had the potential to strengthen Nottinghamshire's dreadfully weak bowling, so that the county engaged him as a bowler in 1899 and he played in five matches for the first eleven.

It was thought he had the accuracy and the strong physique at over 90 kilograms (14 st) to succeed but lacked any spin whatsoever and thus could never beat even ordinary batsmen.

However, the following year his solid defence saw Iremonger establish himself in the first team as a batsman, but he was routinely criticised for lacking strokes and his figures with an average of only around 18 bore this out.

Nevertheless, Iremonger always remained an extremely useful and obdurate bat in any crisis, and even in the wet summer of 1912 where he only once exceeded fifty, eight not outs gave him an average of 26.

The exceptional summer of 1911, though it was thought batsmen "did not find him difficult",[2] saw Iremonger's nagging perseverance on the hardest of pitches rated so highly that he was taken to Australia for bowling alone.

His last season of 1914 saw Iremonger frequently captain Nottinghamshire in the absence of any available amateur to carry out the job, and he regained some of the batting form of ten years before.