Eighteen bowlers returned to individual training last week with a focus on red-ball cricket, and a further 37 names have been added to that list.
Players have not yet been named with specific formats in mind, but the longlist will be the source of the squads for the Test series against West Indies and ODI series against Ireland.
Ben Duckett, Sam Billings, Reece Topley, Liam Livingstone, Mason Crane and David Willey are among those who have been named after a spell out of the international fold, but there is no room for Hales or Plunkett in the group. Others to miss out include Sam Northeast, Tom Abell and Jamie Porter.
"It's really pleasing to be in a position to have players returning to training and a huge amount of work has been done by many to get us this far," Mo Bobat, the ECB's performance director, said. "The pool of players will give selectors strong options when it comes to selecting squads across formats further down the line, as we move closer to our aim of playing international cricket this summer.
"We will need to continue to work closely with our medical team and government to ensure that our return to training and play activities are in line with best-practice guidelines. We're also really grateful for the positive and collaborative response from our county colleagues who are doing a great job at facilitating coaching and support for the players. The fact that we can call on our network to support the national effort shows the strength of our system."
Hales has not been involved with England since being dropped before the World Cup last year, following a positive drugs test, with England captain Eoin Morgan saying earlier this week that it "might take some more time" for him to be reconsidered.
Plunkett, 35, lost his central contract a few months after playing a key role in England's World Cup win. Clarke, like former Worcestershire team-mate Kohler-Cadmore, was stood down from Lions duty last year after revelations concerning a WhatsApp messaging group during the trial of Alex Hepburn. It was recently revealed that Hepburn is appealing his rape conviction, with the hearing set for next month.
England training group: Moeen Ali (Worcestershire), James Anderson (Lancashire), Jofra Archer (Sussex), Jonny Bairstow(Yorkshire), Tom Banton (Somerset), Dom Bess (Somerset), Sam Billings (Kent), James Bracey (Gloucestershire), Stuart Broad (Nottinghamshire), Henry Brookes (Warwickshire), Pat Brown (Worcestershire), Rory Burns (Surrey), Jos Buttler (Lancashire), Brydon Carse (Durham), Mason Crane (Hampshire), Zak Crawley (Kent), Sam Curran (Surrey), Tom Curran (Surrey), Liam Dawson (Hampshire), Joe Denly (Kent), Ben Duckett (Nottinghamshire), Laurie Evans (Sussex), Ben Foakes (Surrey), Richard Gleeson (Lancashire), Lewis Gregory (Somerset), Sam Hain (Warwickshire), Tom Helm (Middlesex), Will Jacks (Surrey), Keaton Jennings (Lancashire), Chris Jordan (Sussex), Tom Kohler-Cadmore (Yorkshire), Dan Lawrence (Essex), Jack Leach (Somerset), Liam Livingstone (Lancashire), Saqib Mahmood (Lancashire), Dawid Malan (Yorkshire), Eoin Morgan (Middlesex), Craig Overton (Somerset), Jamie Overton (Somerset), Matt Parkinson (Lancashire), Ollie Pope (Surrey), Adil Rashid (Yorkshire), Ollie Robinson (Sussex), Joe Root (Yorkshire), Jason Roy (Surrey), Phil Salt (Sussex), Dom Sibley (Warwickshire), Ben Stokes (Durham), Olly Stone (Warwickshire), Reece Topley (Surrey), James Vince (Hampshire), Amar Virdi (Surrey), David Willey (Yorkshire), Chris Woakes (Warwickshire), Mark Wood (Durham)