The principle argument is still preserving Britain's sovereignty, right?
Especially in terms of trade?
Including product safety, working conditions . . . everything?
In the US the commerce clause (Congress shall have power "To regulate Commerce with foreign Nations, and among the several States, and with the Indian Tribes") is the source of much regulation. Anti-trust, civil rights, harbors, airports, drugs. Hard to believe that EU membership means all that. There is no federal government of Europe.
What are the particular aspects of sovereignty which the EU is thought to threaten?
The argument can't be that agreement to be bound by others is objectionable per se. That would mean no trade agreements of any kind.