Vice President Bush, challenged here tonight by a member of Britain's antinuclear movement, responded with an emotional defense of U.S. arms-control policy that drew applause from a large audience of foreign-policy specialists.

Bush, who had just delivered an address to some 1,000 members and guests of England's Royal Institute of International Affairs, was asked by an official of Britain's Committee for Nuclear Disarmament why the United States does not end the "grotesque overkill" of weapons deployment and agree to a multilateral freeze on nuclear arms.

Bush responded that a balance of atomic power is a surer way to keep the peace than the kind of imbalance that now exists. "Balance is the way to deter war and keep the peace," he said.

"Do you think we don't want peace?" Bush asked. "Do you think we care less than others about a nuclear war?"

Bush referred to a few hundred demonstrators outside the meeting hall protesting against the scheduled deployment in Britain, beginning in December, of 112 new U.S. cruise missiles.

He said it was right for those demonstrators to protest because everyone is concerned about nuclear weapons. He also said people cannot protest in communist eastern Europe and that it is wrong to assume that he had no feeling for what the demonstrators were saying. "I can see my own sons out there," he said.

Bush then defended President Reagan's zero-zero plan for eliminating intermediate-range nuclear weapons from Europe. "I think every churchman, every young person, should join" the movement that would support a plan to banish these weapons, he said.

The Soviets have flatly rejected Reagan's proposal, arguing that there is already nuclear parity between East and West in Europe and that the new American missiles will upset that balance.