I don't know (or much care) about non-violent muggings, but murder and violent crime are far more common per capita in the USA than in the UK. The UK has high a high violent crime rate by Western European standards (who generally also prohibit the carrying of firearms by civilians) but not by American standards.
United Kingdom and United States Compared by Crime: NationMaster.com
It's always interesting when people pull up statistics because I have to bring up other facts that can make people feel uncomfortable because they have been taught to feel a certain way even though what they know and observe is different.
The US will have for the near future very skewed statistics based on our western counterparts because we have a larger former slave population that is massively disproportionately violent. Ghettos, 'urban culture', their music is plagued with violence and thuggery.
Blacks are responsible for the majority of murders in the US. Yes, 52.5%. They make up 12-13% of the population and account for over half of murders. That's huge.
This has nothing to do with race, but the culture that developed as a result of slavery, racism, and oppression. I am sure someone will or wants to respond to me telling me I am all wrong, but they know they would never pull over into an East Saint Louis gas station, wander around Detroit, south Chicago, the wards of Houston, and most of New Orleans at night, or even the day for that matter.
The US also has a land border with Latin America, also responsible for large crime elements. People cannot walk from central America to the UK.
Latinos make up the largest group of gang members, followed by blacks. Despite the fact the whites are the majority.
If you were to exclude the differences between the US and the Europe, you'll find no differences. People can get upset when one talks like this because they cannot disassociate race with culture. The US has higher crime rates because we have groups that Europe does not have.