The British have long had a debate on whether or not they need to keep nuclear weapons or not. It is currently quite costly for them to maintain a nuclear arsenal as well as keeping it updated (the current plans for Trident and the submarines to use it is expected to run around 15 billion pounds).
Many Brits have been asking, "why?"
The Labour Party long supported unilateral dismantling of the UK nuclear arsenal, but that policy changed under Smith's leadership as well as Blair's. Right now it is more of a question of keeping defence contract jobs than it is whether or not their is a real need for nuclear weapons. The British have far fewer nuclear missiles than the French and are generally protected by the Americans anyway.