It seems to me, and some others here, that Mr Johnson simply hasn't thought this through.
In practical terms, we would have to define what Islamic radicalism actually means. If it is the support and commission of terrorist acts, that's one thing - but that's a crime...and there is already processes in place to deal with the children of convicted criminals.
But then there's the question of the terrorist father with a wife who knows nothing of his actions until he's arrested. Should her children be put into care? Or would it make more sense for an exclusion order to be placed on the father?
And why just the children? What would the stance be if someone's cousin is convicted of a terrorist act? Mums and dads can be influential, but so can brothers, and uncles, and aunts, and sisters...
So...do we swoop in an remove all minors in the immediate and extended family into care?
Perhaps this needs more thought from our Mayor.
Boris has taken a couple of stands/initiative for which I applaud him (the banning of the gay-cure adverts and the introduction of the bike scheme in London), but I think he is off base on this.