as there are massive problems with Islam in the world
Actually, there are massive problems with people believing that complex conflicts and issues have pat, soundbite causes and not bothering to educate themselves further.
Mainly because while they can see the West as complex and nuanced, they consider vast tracts of the world to be populated by lesser folk, who are only capable of carrying a single thought in their head.
If you think that the conflicts in Syria, Iraq and Libya are the fault of Islam, then you are hugely ill-informed about all three.
Even the rise of IS is far more politically complex than you are probably aware of (clue: IS in Iraq is largely led by people who were formerly commanders in Saddam's army and leading figures in the Iraqi Baath party. Why might that be? The rise of IS in Syria was greatly helped by Assad. Why might that be?)
Therefore it is hugely unfair to place any burden on Sadiq Khan, or any British Muslim to change your attitudes towards Islam, rather then addressing your own ignorance concerning what is actually happening in the wider world.