Interesting link, a few comments from the Czech point of view.
We have actually overreported number of murders. It took me a while to find out why the statistics have so widely different numbers, but in the end I realized that police counts as murders and attempted murders in the same bracket. So that is why we have about double the number of “murders” than what the number of murder victims is.
As regards under reporting of lesser crimes, I know it very well from the Czech Republic. On paper, Prague is the place with highest crime rates, but that is because this is were most new and motivated cops serve. There are several (not many) places in the country where the likelihood of becoming a crime victims is much higher, like the one where I grew up. Unfortunately during time people become accustomed to the ever-present petty and not so petty crime and inability of police to deal with it that they simply stop reporting anything but the most serious cases. They mostly just think that having to spend 3 hours at police station dealing with paperwork and waiting to be processed would just add insult to the injury and prefer to go on with their lives. And that in turn makes the criminals aware of low possibility of the crime being even reported, not to mention being caught, and drives their appetite higher. I honestly believe that the knowledge of criminals that they might be met with deadly force (typical CCer is a guy in his 60s-70s taking a dog out on a walk at 10 PM) is one of the main reasons why the crime mostly remains petty and without serious physical violence in places like my home town.
Also, I had a couple of friends who lived in Brussels and who were victims of crimes multiple times there. For example one Slovak friend (girl) had her apartment burglarized. She came home, doors were kicked in, and she did not know whether anyone is still inside. She called cops and described her situation … and spent 40 minutes waiting for two cops to come. They looked inside, found no-one, and refused to write it down saying that this happens all the time and it is only loss of time to write a report when nobody was physically injured. They’d quite possibly not only lose their jobs for this in my country, but maybe even face criminal charges for obstruction of justice and misuse of official powers.
So UK is far from being the only country with widespread policy of under reporting.