DasK, this is really new to me. It appears that the wine is coming through the cork and not around it. A few questions may help us help you. What size cork did you use? They appear to be 1 3/4" long but are they #8 or #9? What did you use to insert the cork, i.e. a hand corker, floor corker, etc? Did you do anything to the corks before inserting them, e.g. boil them (hope not!) or soak them in k-meta? What brand of cork are you using or where did you buy them?
The cork you are using is made up of coarsely ground cork and a binder. Something appears to have degraded the binder.
BTW, as I see the bottles standing, I agree with JohnT. They need to be fuller (something above the shoulder of the Bordeaux bottle that you are using). A finger width is good depending on how large your fingers are. I don't think the low level in the bottle is realted to this problem.