I figured you'd follow the links and actually take some time to learn about the topic, so I don't think it's disingenuous of me to have left things where I did. Had you taken the time to read through the links, it would be apparent that the everyday sort of corporate management arrangement you're painting it as is not at all representative of the reality here, and that the police force is run not just by the Corporation, but also by the corporations. To quote from near the top of the page that you'd have reached with my link:
Both businesses and residents of the City, or "Square Mile", are entitled to vote in elections
Well now, that sounds interesting, doesn't it? To provide more details from the link that the OP gave earlier:
The City has a unique electoral system. Most of its voters are representatives of businesses and other bodies that occupy premises in the City. Its ancient wards have very unequal numbers of voters. In elections, both the businesses based in the City and the residents of the City vote.
The principal justification for the non-resident vote is that about 330,000 non-residents constitute the day-time population and use most of its services, far outnumbering residents, who number around 7,000. Nevertheless, the system has long been controversial. The business vote was abolished in all other UK local council elections in 1969.
A private Act of Parliament in 2002 reformed the voting system for electing Members to the Corporation of London and received the Royal Assent on 7 November 2002. Under the new system, the number of non-resident voters has doubled from 16,000 to 32,000.
Which is to say that businesses control about 32,000 votes compared to the residents' 7,000, with the larger businesses getting more votes on account of their having more employees. Those elections dictate who gets elected to the Common Council, and the Common Council is the body that has authority over the police force.
So, in a very real sense, the entrenched corporations have direct control over the elections, allowing them to put the people they want in power. Suggesting otherwise is to deny the obvious.