Dubbed "Dad's Army" on account of their advanced age, the gang stole £14m worth of goods from the safety deposit.
They received prison sentences of six and seven years in March.
Nip Tuck's Joely Richardson, Downton Abbey's Matthew Goode, Game of Thrones' Clive Russell and True Blood's Stephen Moyer are also in the cast.
The film, directed and co-written by Ronnie Thompson, has begun shooting and will be released later this year.
It also features David Calder, who appeared in Lady in the Van, Sarah-Jane Crawford and Mark Harris.
The movie is one of three being made about the robbery.
Screen Daily reported in January The Hatton Garden Job was being made by Working Title Films and in May it said The Hatton Garden Heist was being directed by Gabe Turner.
Former EastEnders stars Larry Lamb and Phil Daniels are starring in The Hatton Garden Job, a film about the 2015 London jewellery heist.