Peach was born in Toronto, Canada to parents from Nottinghamshire, England. When he was three years old, the family returned to Britain and lived in Oadby, Leicestershire where his father worked as an estate agent. He attended Wyggeston Boys Grammar School and Oakham School.
Peach married twice. With his first wife, Marina, he had five children before she died in 1913. In 1915, he married Mabel Watson.
Peach died on 24 January 1936 at his home in Leicester. He had suffered from neuritis throughout his life and periods of ill health during the 1930s.
After leaving school, Peach worked with his father for a short time before opening a specialist bookshop in Leicester dealing in manuscripts and early printed books.
By 1906, Peach's eyesight was failing and he gave up selling books. In 1907, he set up Dryad Furniture to manufacture cane furniture with his friend Benjamin Fletcher as the main designer and a workforce of four. At the time the market was dominated by European manufacturers and Peach and Fletcher wanted to develop the local cane industry to compete and supply furniture suitable for the English market. Dryad supplied deck lounger chairs for White Star LInes ships, including the Titanic.By 1912, the company had expanded to a workforce of 50 and moved into larger premises where he established Dryad Metal Works to supply architectural and household fittings manufactured in copper, brass and wrought iron. Fletcher had introduced Peach to the writings of William Morris and William Lethaby and other members of the Arts and Crafts movement and many of the Dryad designs were in the arts and crafts style. By 1914, the companies employed nearly 200 staff.
During World War I, Peach began promoting craft work as a form of occupational therapy for wounded and disabled servicemen and donated large quantities of cane offcuts for this purpose. Identifying the growing demand for craft materials for domestic and educational purposes, Peach established Dryad Handicrafts to supply materials, instructional leaflets and designs and organise classes. By the time of his death, Dryad Handicrafts was the largest supplier of craft materials in the world.
Following his death, the Dryard companies were run by his eldest and youngest sons, Geoffrey and Roger Peach.
Peach and his first wife were involved in social reform and politics and were members of the Independent Labour Party. In 1906, to support Ramsey MacDonald's campaign to be elected as one of Leicester's members of parliament, Peach organised an exhibition on the poor industrial working conditions in the city. Marina Peach was also involved in the suffragette movement and campaigned for the improvement of health care for working class women.
In 1915, Peach was a founder member of the Design and Industries Association (DIA). The DIA was set up to promote better relationships between manufacturers, designers and retailers and to "foster a more intelligent understanding amongst the public for what is best and soundest in design" and was inspired by the Deutscher Werkbund's 1914 Cologne exhibition.
Peach was also active in campaigns to preserve the countryside and prevent the uncontrolled expansion of towns and cities and unregulated advertising. He was the secretary of the Leicestershire Footpath Association from 1912, a long-term member of the Commons, Open Spaces and Footpaths Society and was the Honorary Secretary of the exhibitions committee for the Council for the Preservation of Rural England (now the Campaign to Protect Rural England), for which he organised many exhibitions and lectured. The DIA's 1930 yearbook edited with Noel Carrington and titled The Face of the Land brought his proposals together.
Peach was involved in the founding of Leicester, Leicestershire and Rutland University College (now Leicester University) and served on its board of governors. He was a major benefactor of the college and material he donated to the college forms part of the University Library's core special collection. The School of Law's library is named after him. After his death a memorial fund was raised which funds the biennial Harry Hardy Peach Lecture.
A collection of handicrafts amassed by Peach was given to Leicester Museum in 1969.