Laird commissioned Gillespie Graham, a leading Edinburgh architect, to lay out a square and surrounding streets like Edinburgh New Town. Graham's design envisaged long and straight wide avenues lined with elegant town houses. Hamilton Square would be located where it would get the maximum benefit from the area's topography. This would ensure it would be visible from the Liverpool waterfront emphasising Birkenhead’s civic pride. Work started on the eastern side of the new town around Hamilton Square in 1825. However, due to the economic depression throughout the mid 19th century, this would become the only part of Graham's plan to be fully completed. The square's name is taken from the maiden name, Mary Hamilton, of the mother of Laird's wife, Agnes MacGregor; Mary's brother William Hamilton was also one of Laird's business partners.