Rumors that the Rev. Sun Myung Moon is planning to move the headquarters of his controversial Unification Church from the United States to Britain are "totally unfounded," Moon's attorney told an immigration appeals tribunal here.

The denial was made by James Fox-Andrews, who represented Moon in his appeal against a decision of the British Home Office not to allow him to extend his stay in Britain. The Unification Church leader originally was granted a two-week visitor's permit. It expired in May and Moon is still in Britain.

After a long hearing, a court here ruled that Moon could stay in England for "the time being," and one of his associates said Moon would leave the country Sept. 19.

Fox-Andrews said that there had not been a single transfer of top or middlegrade staff from New York and that there was not truth in a U.S. newspaper report that the church headquarters was being moved to Britain. He also said no American authority had refused to consider the church a charity.

He said there is "no doubt at all that Mr. Moon will leave this country on Sept. 19 or before." he added.

Vivian Reynolds, speaking for the Home Office, said the authorities must be satisfied that Moon would leave at the end of his permitted stay. He noted that Moon had said he wanted to stay two weeks, then changed it to two months, and was now requesting to stay for six months. "How could anyone be satisfied that he intends to leave at the end of the period granted?" Reynolds asked.

Moon did not appear at the hearing, nor did three aides who arrived with him in May. They too have appealed against the Home Office's refusal of an extension of their visitors' permits.