Colossus was designed during World War II for one purpose -- decoding top secret encrypted messages sent by Germany using the Enigma Machine. Germany thought their messages were safe, but the Allies had cracked the code using these computers, and were therefore able to win the war. The Colossus was purpose built, is not a general purpose computer but instead performs a specific processing task. Several instances of the Colossus was built during World War II.
The Harwell Decatron was designed to automate mathematical computations which it did for several years.