Are you sure that this is an English surname? I can't find any evidence. According to the "Geogen" website there is one Irex in the German telephone directory, and the familysearch databank records one Irex marriage in 18th century Cologne.
I wonder if the name Irex Road, Lowestoft, commemorates a shipwreck, see here -
http://www.backofthewight.co.uk/irex.htmPerhaps the ship or the crew had a Lowestoft connection.