One way Great Britain attempted to limit Hitler's sphere of influence was

Hitler wanted to expand his influence to the East, and Italy, Nazi Germany's main ally, wanted to expand its influence all over the Mediterranean Sea.

What Britain did was to use the colonial power it had in the Middle-East, especially in Egypt, to prevent Germany and Italy from conquering Northern Africa, the Middle East, and other eastern regions.

This proved successful because Britain was able to hold back Italy and Nazi Germany (Nazi general Erwin Rommel was defeated in Northern Africa by British forces).