So much for the large-scale Muslim plot to take over various British schools being solely about "extreme Islamists".
The Muslim Council of Britain (MCB) is the most "mainstream" Muslim organization in the UK. Indeed the British government of the time (New Labour) helped fund and set up in 1997. Some of its leaders have written articles for the Guardian, the Huffington Post and they've also been featured on the BBC (e.g., Inayat Bunglawala and Muhammad Abdul Bari – both mentioned below).
This is what the MCB says about itself on its website:
"The Muslim Council of Britain is one of the UK's largest and most diverse Muslim umbrella organization with over 500 affiliated national, regional and local organizations, mosques, charities and schools."