Henry Hedderwick was a well-respected member of society, active in legal education and municipal affairs.
In the early 1860s, he established a legal practice in Melbourne with Charles Palmer. From 1870, Hedderwick carried much of the partnership load at the firm.
It was involved in extensive conveyancing work and prospered during the late 1800s, in the heady years of Melbourne property development. As the city grew and its economy diversified, the firm's work evolved, changing from conveyancing and managing family estates and trusts, to a predominantly commercial practice.
In addition to his legal work, Hedderwick was the mayor of Kew between 1873 and 1875.
He was also a founding member of the Australian Club and a member of the council of the Law Institute of Victoria.
In 1984 Hedderwick Fookes & Alston merged with another Melbourne firm, Arthur Robinson & Co, to form Arthur Robinson & Hedderwicks. In 2001 that firm merged with Sydney firm Allen Allen & Hemsley to form Allens Arthur Robinson. Today, the firm is known as Allens.