Here's the information about immigration and crime in the UK.
https://en.wikipedia.org/wiki/Immigration_and_crime#United_Kingdom
A few takeaways:
"In total, foreigners represented 13% of the prison population, whereas foreign nationals are 13% of the total population in England and Wales."
"Research has found no evidence of an average causal impact of immigration on crime."
"A 2008 study found that the crime rate of Eastern European immigrants was the same as that of the indigenous population."
If you Google around the topic, it's interesting to see that the newspapers that are traditionally "anti immigration" are delighted to use the numeric rise in immigrant
crime levels as a splashy headline, without pointing out that it's no greater than the rise in immigrant
numbers or that immigrants are just as likely/unlikely to be criminals as Brits.