Rhodes, who had been in the post at the London-based children's charity for 15 months, said in a statement that it was with "great regret" that she was to leave.
"Although I have been very happy here, I have come to feel that there is a divergence of opinion between the governors and myself about the future direction of the charity," Rhodes said.
Asked about the disagreement between Rhodes and the governors, Coram Family's chair, Sir Christopher Benson, said his interpretation was that the governors had wanted to work in line with a consolidation strategy that was laid down in 2002. However, Rhodes had wanted to expand activities beyond this remit.
"My guess is that Honor had territorial or geographical ambitions that went beyond London," Benson said. "The governors think the current core platforms are what we are best at and what we should concentrate on."