This is what we use, Thomas. It works and doesn't have chemicals. You could also pull as much of the creeping charlie out by hand, then spray the stems closer to the ground.
Do not use the above recipe on lawn. Will kill it.
I also suffered with Creeping Charlie! At one point, two thirds of my lawn was taken over. I tried everything under the sun. I finally tried Spectracide Weed and Feed. I mixed a much stronger solution than the instructions said. Used a handheld sprayer and really wet the "lawn" down with no rain scheduled for the next few days. Killed the Charlie and he lawn came back stronger than ever. I still get some Charlie coming back every so often, so I pull out what I can and spot spray it along with other weeds as general maintenance.