LONDON—The police here have dropped a yearslong fraud and corruption investigation involving a major brokerage company after the firm, Tradition Financial Services, stopped cooperating with investigators, according to people familiar with the matter and correspondence reviewed by The Wall Street Journal.

The City of London Police, which investigates financial crime, opened a criminal investigation around 2011 into potential improprieties involving lavish spending and attempts to win overseas business by a number of Tradition...