All aspects of a Muslim's life are governed by Sharia. In the Islamic tradition Sharia is seen as something that nurtures humanity. They see the Sharia not in the light of something primitive but as something divinely revealed.
Whilst us in the West would see a draconian, medieval practice full of beheadings, stoning and amputations, Muslims see the Sharia regulating all human actions and puts them into five categories: obligatory, recommended, permitted, disliked or forbidden.
In Arabic, Sharia means the clear, well-trodden path to water. Islamically, it is used to refer to the matters of religion that God has legislated for His servants. Thus it is seen as divine guidance.
It is the aspects referred to above that determine we could not alllow a two-tier legal system to evolve or exist, since elements of sharia have no place in a humanitarian society. Not just the hadd penalty aspects (execution, amputation and public floggin), but also the penalties for adultery (100 lashes or stoning, or death if caught in the act by 4 people) and the obligation of a husband to beat his wife into submission and model behaviour.
It is likely that many Muslims in the UK would be in favour of Sharia law being implemented here, but true Sharia law is only really possible in a Muslim society, not in a non-Muslim or mixed society. Flogging for public drunkenness might make some of our binge drinkers think twice before acting as they do.
It would be interesting to see though, whether those (non-Muslim) people who think that we should "bring back hanging" or reintroduce capital punishment would be as eager to see the ful effect of something like sharia law. A short excursion around chop chop square in Riyadh, soon puts that right.