The countries with lowest crime numbers in EU per capita are (ordered by crime rate increasing): Slovakia, Hungary, Estonia, Cyprus, Slovenia, Czechia, Poland, Bulgaria, Croatia, Lithuania, Romania.
All of them are socially pretty homogenous. Most of them escaped Soviet block. Some even escaped Soviet Union. On the other hand, look at the countries from the other side of chart (this time, rate decreasing): Belgium, Spain, Portugal, Sweden, Luxembourg, Netherlands, Germany.
As this data concerns only EU, there is no UK here, but as I remember, it had around 3x crime rate as the Republic of Ireland, which would put it on the tops of the EU list.
Of course, increased diversity might not be the only differentiator between the countries from the top of the list and those from the bottom, but I think it defeats your point (almost as if you were racist for having irrational fears against living in a post-soviet society, which aren't backed by numbers).