Muslims are arguably even more divided among sectarian lines. Half of the violence in the ME now is related to the Sunni/Shia rivalry. As to London, hove you not considered that Sadiq Khan was elected because people actually support what he stands for, as opposed to a small minority of Muslims that conspired to have him elected?
Muslims may be divided in the Middle-east and South Asia, but they are united against the common enemy (native whites) in Europe. The Muslims communities in London and the other parts of England are mostly homogenous ones, populated mostly by Sunni Muslims from Pakistan and Bangladesh. There is not much sectarian division among them.