The British Crime Survey has for many years been presented to the general public in a rather misleading manner as though it provided definitive figures for the level of crime in England & Wales. In fairness this is not a claim those who carry out the survey would make, but one that is made by the Home Office to the press, for example by saying that the BCS 'measures the amount of crime in England and Wales'. As journalists are mostly arts grads who flee in terror when confronted with a statistical survey, this claim is generally accepted or dismissed entirely based on their existing predjudices.
Why the BCS is not a comprehensive measure of crime.
The BCS doesn't cover certain categories of crime. Elliott Joseph's post on the BCS for example highlights its shortcomings over crimes that are serious but rare compared to the more numerous petty crimes. It is the more serious crimes that causes public anxiety.
It also doesn't include crimes without single identifiable victims, this means that crimes that damage society as a whole are often unrecorded. When schools suffer arson attacks or shops are trashed this impinges many people's quality of life as much as a crime directly against themselves.
It doesn't cover certain categories of victim. Crimes against under 16s aren't included, despite the fact that teenagers are one of the groups most at risk from crime. Nor are non residents of the UK, so crimes against tourists and migrant workers are not measured.
It is not a truly random sample. A significant proportion of the people contacted refuse to participate, and the refuseniks are more common in areas with high recorded crime rates.
Even on crimes which it does cover it isn't necessarily the best way of measuring them. People in general cannot remember with any great precision whether a crime they have suffered occurred 8 months ago or 14 months ago, so asking people to recall what crimes they have been victims of is not going to produce an accurate figure. In 'Crime and Human Nature' the authors refer to a study that was carried out in the San Jose, California found that of people who had reported an assault to the police in the previous twelve months on 48% recalled an assault when interviewed for a crime survey. The figure was particularly high if the reported assailant had been a relative.
All of the above factors are limitiations of crime surveys, not a reason to ignore them or to suppose that recorded crime figures give the full story instead (they are equally problematic). However there are unfortunately a lot of know nothing pundits, politicians and bloggers who make preposterously sweeping claims about Britain's crime levels based on it.