Yes there are these tendencies in the censorship, but they're ultimately meaningless. The UK is a much more violent society than the US, statistically. That is real and meaningful. Who gives a crap about the differences in how movies are rated.
That's not true. What nonsense statistics are you using? There are dozens of U.S. cities with higher per capita murder rates than London or any other city in the UK. How quaint it is to contradict someone with vague and controversial statistics.
Murder rates are higher in the US, but murder is a small fraction of violent crime. All other violent crime is much more common in the UK than in the US. In my own personal experience it's also much more indiscriminate in the UK. It's rather easy to avoid trouble in the US, whereas you have high rates of home invasion in the UK in middle class neighborhoods, for example.
Do you have a link to these stats? I don't think most people in the UK would even know what an home invasion is (I know from Ice-T) and Wikipedia claims it is notoriously hard to get stats this topic since it's not a defined crime in many jurisdictions.