The only way from City of London to Porz (Rhein) is by flight. You should expect to be able to find tickets starting around $299, if you search flights from LHR to CGN. The best time to book shorter flights is 2-3 weeks before your trip.
On your trip from City of London to Porz (Rhein), it is best to book as soon as possible. It won't necessarily help reduce your price by a large amount, but will ensure that you have a spot on the bus or train.