UK's Nuclear Deterrent

Towards the end of her speech, the Prime Minister mentioned the nuclear non-proliferation treaty and multilateral disarmament. I was interested in that. Surely we should start from the basis that we want, and are determined to bring about, a nuclear-free world. Six-party talks are going on with North Korea. China is a major economic provider to North Korea. I would have thought that the relationship with China and North Korea was the key to finding a way forward.