Man On The Beat / The Police - 1945 British Council Film Collection
http://www.youtube.com/watch?v=TC2e-958r7E
A fascinating look at how the British police were represented in the mid-20th Century

The Police-It's Our Job Documentary https://www.youtube.com/watch?v=aRxvYUw0Q6U 
A documentary from the early 1960s that focuses on the modern scientific technology underpinning contemporary police investigation