Coram established the museum in 1998 to care for its Foundling Hospital Collection of art works, which includes sculptures, manuscripts and paintings by William Hogarth, including his portrait of Captain Thomas Coram.
A legal ruling by the Attorney General when the museum was set up in 1998 gave it 25 years to raise funds equivalent to the market value of the collection.
Coram set up the Foundling Museum as a separate charity because its articles did not give it the power to administer an art collection.
The museum’s annual report for 2011/12 says that Coram has the power to appoint four of the museum’s 10 trustees.
The Guardian reported that Coram changed the museum’s articles last year to allow it to remove trustees.
On 23 May this year, Coram informed six trustees by letter that they had been sacked, including Jeremy Deller, a Turner Prize-winning artist.
The museum confirmed the removal of the trustees. "The work of the Foundling Museum continues as usual," said Caro Howell, director of the museum.
Coram confirmed it had removed the trustees but declined to confirm whether it had changed the museum’s articles last year to enable the removals to happen.
"Some former trustees of the Foundling Museum felt things should be done differently and their opinions were, in view of the advice to the Coram board, considered incompatible," a spokeswoman for Coram said.
A spokesman for the Attorney General confirmed his office had written to Coram at the behest of the museum’s trustees.
"This office wrote to Coram to raise various provisional concerns," he said. "The AGO asked the foundation to provide further information in relation to those concerns."
Others in the art world have expressed concern about the removals.
"I am extremely worried for the future of the museum," said Sir Nicholas Serota, director of the Tate. "It has flourished and been extremely well led by its trustees and director."
The Art Fund, a grant-making charity that donated £100,000 to the museum to help purchase for the collection The March of the Guards to Finchley by Hogarth, also expressed concern.
"As a charity and funder of the museum, we’re deeply concerned about the apparent goings-on," said Stephen Deuchar, chief executive of the Art Fund. "We want to know what Coram’s motivations are behind the removal of the museum’s independent trustees and what it has to say to those of us who have supported the museum over many years."