As for the stats, it'll be pretty accurate. Pregnancy levels are known, crime levels are known (if slightly altered), immigration we have a fair idea about (coming in, not going out), benefits are about right (we used to say £10 of your monthly wage went to fraud when I worked there)...
As for the 1000 people doing the survey, that makes it +/-3%. So not bad, enough that it says people are wrong.Though the weighting lowers that, but still not terribly inaccurate.