Once qualified as a lawyer, Hendy established a law centre, the Newham Rights Centre in East London, and worked there full-time for three years. He then lectured for a year at Middlesex Polytechnic, before returning to the Bar in 1977 and focusing on personal injury and industrial relations cases.
In the mid 1980s he successfully represented Wendy Savage, a consultant obstetrician and gynecologist who was suspended from practice for alleged incompetence. The case lead to him working on others in the area of medical negligence.
In 1984-5 he represented the National Union of Mineworkers in the civil litigation arising out of the Miners' Strike. He took silk in 1987. In 1991, he was one of four QCs, along with Michael Mansfield, Geoffrey Robertson and Kevin Garnett, acting for the National Union of Mineworkers against claims that had handled funds inappropriately during the miner's strike of 1984–85. In 1992 he represented mining unions at the High Court against attempts to close 31 coal mines.
In 1995, he acted for National Union of Journalists (NUJ) member Dave Wilson in the Wilson and Palmer v United Kingdom case that ended discrimination against trade unionists.
In April 1999, he took over as head of Old Square Chambers, replacing John Melville Williams. By that year, seventy-six of his cases had made it into law reports.
He is well known for representing the relatives of the victims of the Ladbroke Grove and Southall rail accidents.
He retired from head of Old Square Chambers in 2009.
In 2011, The Lawyer labeled him the "barrister champion of the trade union movement", noting that he often assists Unite, ASLEF and the National Union of Rail, Maritime and Transport Workers
He represented the NUJ at the Leveson Inquiry and questioned Rupert Murdoch directly on 27 March 2012.
His mother was the youngest daughter of the 6th Baron Wynford and his father was "a communist electrician and trade unionist". He describes his father as "a great fighter for human dignity as a trade unionist" and as being the greatest influence on his life. His brother is Peter Hendy CBE, the commissioner of Transport for London.