Imperial is a world renowned uni especially for Engineering. LSE is also a very good uni with a great reputation! Queen Mary/Kings and UCL are also good universities however i would say a different level to Imperial and LSE. My cousin goes Queen Mary and she loves it , has a campus unlike a lot of London unis which is a great experience.
Check out comparetheuni.com they have a good head to head system where you can compare unis side by side. Its pretty good if you want to compare unis quickly.