Listen to Thabet
"It should be realised that the shari'ah is not a single text that is opened and from which one reads an answer to a particular situation. To talk of "shari'ah law" is really to talk of the cumulative interpretation of a whole range of texts and customs, foremost of which are the Qur'an and hadith material. It can be seen as a combination of practice, theory, belief and custom. A social history of Muslims could be written using these interpretations as the shari'ah has developed depending on the situations (cultural/geographical/social) in which Muslims have found, and continue to find, themselves. It does violence to the concept of shari'ah to reduce it simply to a set of 'laws' to be enforced by the state, which is what is assumed by far too many people, including Muslims. When Western Muslims talk about shari'ah they are not likely to be referring to the functions of the state or seditious activites which undermine the state or society at large; but about individual matters of conscience, piety and observance of religious duties."
I once wrote a post on shari'a, and think there is a bit more to it than that, depending on how you view issues such as ijtihad. The point stands, however, that these polls are useless unless you also find out what people mean by shari'a, and I trust that Thabet is close enough to the pulse of Islam in Britain to give a good read on what is happening.