It has been proven that (if conducted corrreclty) asking a thousand people can be extrapolated across the country to an accuracy of a couple of percent.
From the Mori-ipsos website:
Q9 How can you be so sure your surveys are representative of the British public?
To ensure our data are representative, the people who take part are selected very carefully, according to the specific survey criteria. For example, when carrying out a national face-to-face opinion poll, we would randomly select a number of local areas (sampling points) and, within each area, interview a specified number of people (respondents). Respondents within each sampling point are selected either randomly (e.g. conducting an interview at every 'nth' address), or through setting targets (or quotas) on particular characteristics (e.g. age, gender, work status) deemed to be linked to how people might respond to the survey. The sampling points are selected so that, when combined, the total sample reflects the characteristics and opinions of the national population.
http://www.ipsos-mori.com/rmu/faq.shtml