U.N. Ambassador Andrew Young opened his mission to Africa yesterday with talks with British officials in London, and said afterward that his optimism for a quick settlement in Rhodesia had "waned."

"Nobody's given up hope, but nobody expects any easy answers," he said after meeting with British Foreign Secretary Anthony Crosland and Ivor Richard, chairman of the stalled Geneva talks on Rhodesia's future. Young left London last night for Tanzania and Nigeria, to meet with major African heads of state.

Botswana, meanwhile, denied Rhodesian charges that black nationalist guerrillas operating from within its borders had kidnapped 400 school children and taken them to Botswana as recruits for the guerrilla forces.

A Botswana government spokesman said authorities questioned 384 teenage pupils from a mission school in Rhodesia who arrived Monday at Kobojango, a village near the border in northeast Botswana. He said all denied that they had been abducted and none wanted to return to Rhodesia. The spokesman said the youngsters claim they fled to escape harassment by Rhodesian security forces.

In Washington, British Ambassador Sir Peter Ramsbotham met with Secretary of State Cyrus R. Vance to discuss the situation in southern Africa, and British diplomatic sources said Britain may again seek the help of South Africa's Prime Minister John Vorster in getting the deadlocked Geneva talks resumed.

In other developments, the Roman Catholic Church came under strong government attack in South Afirca yesterday for racially integrating its schools there in defiance of the government's policy of a partheid.

Calling the church move "provocative," the administrator for Cape Province demanded government action at the "highest level," declaring: "The authorities cannot be flouted. They must act to maintain discipline, law and order."