IT HAS LONG been assumed that the best way to hide money is to move it offshore. But opportunities for concealment in palm-fringed tax havens have narrowed over the past decade as international financial-transparency agreements have kicked in—including the Common Reporting Standard, a pact involving more than 120 countries to automatically share information on financial accounts. Of the remaining possibilities for shielding assets from prying eyes, one of the most alluring, it turns out, involves using vehicles not in Bermuda or the Bahamas, but Britain.