BASIC was founded as the British American Security Information Council. It is unique in its approach to the problem of nuclear weapons. There are roughly three kinds of organizations that work on nuclear weapons. The first is think tanks that favor nuclear weapons. They tend to be funded by conservatives and press hard to keep nuclear weapons out of any other hands than the ones that already have them. Sometimes they call for increased spending or new types of nuclear weapons. The second group is think tanks that oppose nuclear weapons but focus most of their effort on working to prevent proliferation. This agenda ensures a minimum of friction with governments of nuclear-armed states, like the United States. These groups make up what might be referred to as the anti-nuclear weapons establishment" and garner the lion's share of the funding in the field. The third type is organizations that whole-heartedly oppose nuclear weapons. They tend to be liberal, have little or only grass roots funding, they press strongly for disarmament, they condemn the nuclear-armed states loudly with moral arguments, and they tend to deride the arguments and sometimes the character of those who favor nuclear weapons.
BASIC is unlike any of these organizations. BASIC sees the importance of nonproliferation, it presses for disarmament, but it also sees the importance of sitting down and finding common ground with representatives of nuclear-armed states and those organizations that favor nuclear weapons. BASIC seeks compromise and consensus in a world that has long been polarized. It takes the views of pro-nuclear scholars and spokesmen seriously and treats them with respect. One reason why that works as a strategy is that BASIC does not believe in the outmoded conceptions of nuclear weapons. If the terms of the debate are wrong, then likely all sides will have to rethink their positions before progress can be made.
You can read more about BASIC's unique approach to this issue here