There aren't enough police to investigate crimes against actual people in London, and I imagine the same is true elsewhere.
They're personal anecdotes but I think they apply;
Guys on a moped tried to mug me for my phone - I kept hold of it and they rode off, 60 seconds later another pair of different guys tried - again I kept hold and they rode off, (never experienced anything like it) I reported it to Shoreditch police station, there weren't any officers around to deal with it, the ones I did find looked like they'd been running a marathon - there were no resources left, it was frankly shocking. I officially reported it, absolutely nothing back from the police, nor have they contacted the premises to get the CCTV footage. (this was all about 3 months ago) nothing at all happened.
In contrast someone pick-pocketed my phone from my bag, I reported it online - I've been contacted about 20 times by all manner of people trying to investigate it, stacks of emails, stacks of phone calls - for something worth a few hundred quid that I had blocked the moment it was nicked, everyone knows it's totally gone.
TLDR
It seems that if you get something stolen and you need a "virtual policeman" to send you emails and stuff, get a crime number for insurance etc, that's fine.. However if anything happens to you physically that requires an investigation - forget it, even if you almost end up under a bus.