If you read the comments on that article, there are a lot of valid points. For instance:
Point 1 - The figure quoted is an estimate only - they cannot really know the true figure. Some benefits are much more likely to be fraudulently claimed than others; while it's very unlikely that the true figure is massively high, it could be higher than the official figures suggest. The people questioned may also be thinking of those claimants who are playing the system while not technically committing fraud.
Point 2 - People's perception will be affected by where they live. In some areas the number of immigrants is indeed very high. If you ask this question of an inhabitant of Slough and one from Skye, you will probably get two very different estimates.
Point 3 - The recording of crimes, and definitions thereof, keep changing. There may also be a possibility that as police stations close, fewer crimes are being reported, especially minor crimes. And again, peoples' perceptions will be affected by where they live.
Certainly, people do need to be better informed; but telling them figures for such things across the whole country will not be believed by those who live at the sharp end of social problems. I suspect some of these apparently wild guesses are the result of real local observation.
Btw i hate surveys. Unless every single person in the country is surveyed then it doesn't really mean much to me to. Carried out on a mere 1,015 people is not enough to start calling the British public wrong.