The statement said Martin - born in the East End of London himself, in Bow - had died on Saturday.
"For over 50 years, Derek was a truly authentic working-class voice in British television and film," it went on.
Meanwhile, his agent said it was "a privilege to be a part of his creative journey" - and said he had "cherished his time portraying Charlie Slater".
"Derek was a devoted father, a generous member of the charitable Water Rats, an avid golfer and all-around good man who will be greatly missed," Henry added.
Martin began acting in the 1960s, having previously worked in factories and as a butcher at Smithfield Market in the City of London.
Despite having no professional training, he went on to appear in programmes such as Doctor Who, Z-Cars, The Sweeney, Eldorado, Law & Order and Hart to Hart, before landing the role of Charlie Slater.