Can a law school's graduate in UK works in the United States?

Not without a lot of extra time and expense. You will need to be admitted to each state's bar separately. You'll need to take classes (between 1 semester - 3 years depending on the state) and pass the bar exam. You'll have to be licensed in each state individually. Your other issue, as a previous response has pointed out, will be getting a visa and/or job. There are plenty of unemployed American lawyers around - no employer is going to spend the time and money to sponsor an attorney who isn't licensed in the jurisdiction. For law it is always best to get the degree in the country in which you wish to practice.

it would be difficult to get a visa. the only realistic chance would be an H1-B visa -- critical skill that can't be filled by US citizens. The employer has to initiate the paperwork, not the person who wishes to be employed. that means you have to find the employer in the US who needs a British trained solicitor, presumably for work involving some form of import or export cases [likely the most frequent kind].