Bill Halson, a businessman, is to lead the charity, whose patrons include Sir Yehudi Menuhin and Sir Harry Secombe and which is dedicated to strengthening the family.
Professor Whitfield, a social policy commentator and also head of St George's House, Windsor, a religious think-tank founded by the Duke of Edinburgh, caused consternation among charity members when he attended a convention in America in August connected with the controversial cult, also known as the Unification Church.
The visit went against reassurances Professor Whitfield made to members five years ago, after previous contact with the Moonies alarmed the charity.
Although he told The Independent that the visit was "purely private business," he then resigned from the charity three days before he was due to face an extraordinary meeting of trustees to explain his presence at the convention.
But the professor said yesterday that he had done the job since 1986 and had many other things to which he wished to dedicate more time. "Ten years is a long time to be honorary chairman of anything."
He would do nothing to support the Moonies in this country, but they had brought together an interesting programme of speakers in Washington. However, as his attendance had upset some of the trustees, it had triggered his decision to leave.
His departure from the National Family Trust (NFT) comes amid growing concern that the reputation of St George's House was suffering under his leadership. It is a centre for training clergy and a forum for discussion, which attracts a wide range of participants up to Cabinet level.
Some of those associated with St George's have echoed the NFT's worries. "The Moonie thing is an absolute disgrace," one said. Another said: "I fear that the Unification Church will want to use the connection with the Royal family."
But the centre also has its own problems. An inquiry last year concluded that Professor Whitfield was not respected or trusted by most of St George's House and "his management style, manner and personality create resentment and an unhealthy working atmosphere".
An insider said: "There have been a number of discussions ... Unless the situation in relation to Professor Whitfield is resolved it will fester."Reuse content