There actually is no level requirement, just finish big ben in the royal musem and defeat meowiarty ( i think thats how you spell it ) on the final floor. He is 2,500 health. At least when i defeated him.
So this is how it goes : Hyde park Chelsea court Ironworks Newgate prison Knights court Katiziens lab Counterweight east Countererweight west Big ben
Tell me if im wrong, Because i haven't been here i a long time. But If your askingwhat level i was when i went to the next world, (Mooshu) i was level 34.