There may be plenty of British Muslims that are perfectly peaceful, want nothing more than to be allowed to follow Islam on a personal basis.
But that isn't where the trouble for democracy lies. This Telegraph article, and this Channel 4 Dispatches programme, show the real intent of many 'politicised' Muslims. But it's not as if being 'politicised' is restricted to a few fundementalists. Islam is both a religious and a political movement, and it's long term intentions are made clear over and over again. And the concept of infiltrating organisations that have views or policies that are incompatible with Islam (i.e. with Sharia) with the intent of taking control and applying Sharia wherever they can, is perfectly compatible with the long term aims of Islam.