Things are reported in the media much more than they used to be: reading the Daily Fail you'd think that urban Britain was overun with Eastern European gangs and Nigerian murderers. All newspapers blare out child abduction, but it remains true that that particular crime hasn't really risen in decades. You are far, far more likely to be a victim of car injury than a crime.
I lived in Hackney for decades, and was mugged once, and verbally abused , once, for sticking my nose in and stopping a kid nicking a bike. Not bad.
That said, I do feel the "petty" crime rises and falls with the economy and treatment / mistreatment of the lower end of the income scale. Under Thatcher, general burglary and mugging type of crimes rose, as did drug addiction etc, and it looks very much like that is on the rise again.
My local police send an email out detailing local crimes, with postcodes. Now, I live rurally now, but it's really not worse than you'd expect, given that there's nothing for the kids to do and a lot of rural poverty and no jobs. Sheds broken into, cars damaged, that sort of thing. What IS rising, is hopelessness, and that does lead to more petty crime.
I don't feel any less or more threatened rurally than I did in an urban setting, and I don't feel crime has increased. I do remember a flood of homelessness in the 80's, as people lose their houses and the mentally ill fell through the initial "care in the community" and I think we will start seeing the evidence of similar moves and cuts soon, so I am fully expecting a rise in petty theft, homelessness, and random attacks and crimes by people who have fallen through the net of an NHS that's been cut to nothing. I'm also expecting a flood of disaffected youth who no longer have a hope of further education, and lots who are left disillusioned by it, in a few years. Much like my youth.....