The vespa breaking system, it definitly isn’t a disk brake, they are a drum brake system common at this model launch date. A steel wire plays an important role in the braking system. It reminds me of my  V-Brake bike, good old technology.

See here for a simple description of the common braking systems available and how it is inside.  http://www.levintirecenter.com/types-of-brakes.html

Vespa 50s Brake