I hold a Norwegian passport. can I apply visa to China from Chinese embassy in UK?

Robert, your proof of legal stay in the UK is required, such as your resident permit for employment or study and valid visa for UK. Anway, I think you may consult with the CVASC branches in the UK directly to confirm whether you can apply. If you can tell where you stay, I may find the contact information for the CVASC that has the jurisdiction in your area.