Robert Farley makes the case:
The debate currently taking place in London matters for Washington, and U.S. defense officials have already expressed concern about the extent of British defense cuts. However, since taking office, President Barack Obama has made global nuclear abolition a central focus of his nonproliferation agenda, both rhetorically and in policy. A decision by the United Kingdom to forego the replacement of Trident and to eschew any other nuclear delivery system would advance this goal enormously. No major nuclear power has ever given up its weapons, despite the formal requirement of the Nuclear Non-Proliferation Treaty to work towards abolition. In the context of growing concern about nuclear proliferation, abolition of British nuclear weapons might provide an important symbol of commitment to Global Zero. However, there's no guarantee that a British policy shift would bring about a change in behavior in North Korea, Iran, or any other nuclear aspirant.Just as important, however, is the money that would be saved from foregoing Trident replacement, which could be spent in other areas.
Yes, but what if Britain decides to eliminate its nuclear deterrent and a new U.S. president assumes office with a dimmer view toward such Utopian optimistic plans for "global zero?" Efforts to slash their arsenal to curry favor with the U.S. would then fall rather flat.