This is just one of those things that you will find in all languages – a phrase that developed a long time ago and is now set in stone. In addition to the previous answers ‘brake’ is not only a verb (= to brake) and “putting the brakes on” a colloquial form with he same meaning but in English the singular is also used as a generic technical term, for example if someone explains the function of it as a mechanical item (as in: “The brake is a device to slow down a moving vehicle.”). But otherwise the plural is used, probably because a car, like in your example, does not have just one brake but four, i.e. one for each wheel. That has also moved into general language. Here ‘putting the brakes on’ means simply to interrupt something or slow it down. You might hear, for example, “He worked all hours but after the heart attack he put the brakes on.” meaning he worked fewer hours and ‘slowed down’ his life style.