Well, you cannot seriously expect to fly for 14.99 GBP on a E135....
Given the limited Lufthansa network at CGN, HAM is indeed the only useful conncetion. Anything else (MUC, TXL) requires a three hour stop-over.
Anyway, for those booking under the LH designator (I assume this is possible), Lufthansa nowadays offers "Rail&Fly" for 19 EUR which allows you to travel on any train to any place in Germany after/before your flight. For example, Stuttgart is little over two hous away from Cologne on the high-speed train, Frankfurt just one hour.