Dueling was always illegal in the United Kingdom, and the constituent nations which made it up prior to unification. Its decline isn't tied to it becoming illegal, but rather public opinion coming to be more inline with the law - juries showing more willingness to convict, and the public showing less interest in shaming someone for refusing a challenge. I've written quite a lot on dueling, and I think this one has the most touching on this specific topic, but suffice to say, the duel had mostly disappeared from English life by the end of the 1840s. Happy to field any follow-ups you might have best that I can.