I would kindly disagree. In my rather "posh" and "good neighborhood " little village I've had 3 house robberies (well, one robbery and 2 attempts) in the span of 14 months, and I have myself witnessed two shop robberies as I was in Sainsburys for milk and eggs.
The crime is there, can be absolutely overwhelming and police does absolute f*k all about it (after the robbery they didn't even bothered to shop up, I was told over by phone to collect the evidence myself and bring it to the police because "we are solving these crimes from the office" by the investigating officer. They didn't solve that one).
Posh might be part of the issue. In my area seems like most home robberies are in wealthy neighborhoods, where no ones home and there might be nice jewelry to steal instead of my sad ancient tv.