British people would never allow Sharia Law in the UK, however look at birth rates & immigration figures for muslims vs emigration of non muslim Brits and lower birth rates, and you realise that it won't be British people agreeing to Sharia Law in the UK, it will be muslims passing it.
Even if you take the white indigenous Brits out of the equation and look at the immigration figures, it becomes apparent that the majority of migrants coming to the UK aren't even Muslim.
Will the hordes of African Christians, Indian Hindu's and Sikhs and Christian Eastern Europeons now living in the UK in large numbers tolerate living under Sharia Law?
There will be around 10% of regions in the UK which will attempt to practice Sharia Law due to high Muslim populations within that region, but it just couldn't be enforced in the other 90% even if the Muslims attempt to do so.