The charity runs projects for people who are disadvantaged in the workplace because of some form of disability, ill health or social circumstances.
The projects include Palmer Gardens garden centre in Trowbridge, Wiltshire, and horticulture projects in Stanmore, Portsmouth and Lincolnshire.
Voluntary sector chief executives body Acevo has called for Charlesworth's reinstatement, and the Charity Commission will meet trustees of the Shaw Trust at the end of September to discuss concerns raised by Charlesworth.
Charlesworth contacted the commission about financial management and governance at the trust after being given notice of dismissal and put on gardening leave.
The trust has declined to say why it has given Charleswoth notice of dismissal but sources suggest there has been a breakdown in his relationship with trustees.