Which agency should British immigrants in Shanghai go to? How much is the agency fee?

Personally, it is better for overseas Chinese immigration agencies to handle British immigration. You can call them to ask about the cost of emigrating to Britain.

In the current British immigration law, the easiest way to become a British citizen is to marry an Englishman. Get a marriage visa for two years as soon as you get married, and then you can automatically apply for permanent residence immediately, and you can get British citizenship in another year. During this period, you can also enjoy social welfare.