It has nothing to do with the Empire, and if as you say you are only first generation British your ancestors or you can't be held responsible for something you had nothing to do with....
Third World definition. "The nonaligned nations — which are often developing nations — of Africa, Asia, and Latin America. They are in a “third” group of nations because they were allied neither with the United States nor with the former Soviet Union." This was all to do with the 'cold war'.