In most (but not all) automotive applications the power socket is on its own circuit. Multiple sockets are generally on separate fuses, but this varies with make and model.
First thing I would do is a visual inspection of ALL the power sockets in your vehicle, starting with the one in the ash tray. Unplug the actual lighter itself if your car has one. If you don't see any foreign objects (coins, etc..) in the socket, remove the socket and inspect the connector at the back, and the socket itself. I have personally seen the sockets themselves short out; the outer part of the socket is ground, and the button in the center is the positive terminal. These are often held together at the rear with a nut, where the positive wire attaches to the socket itself, separated with a thin insulator, I have seen these shift around or overheat, distorting the socket and shorting it. There is also usually (At least on the Japanese vehicles I've worked on; Ford may be different) a fuse at the back of the socket that is part of the socket itself, if this blows the only recourse is usually to replace the socket itself.
You can buy aftermarket add-on 12V sockets that usually come with wiring to connect it, this may be a good option if nothing obvious is found in the above inspection. If you've got a test light or other method of limiting the current as outlined in the above comments, I'd unplug the socket and see if the short is still present, from there I'd get ahold of a wiring diagram and see if there's anything else in that circuit that can be disconnected to test - will tell you where in the circuit the short is. If the socket itself isn't shorted, and it's not otherwise obvious, you may want to just add an accessory fuse and run new wiring to the socket vs tearing into the harness to find the problem. My suspicion is that someone overloaded the socket enough to melt it and short it out, but not enough to pop the fuse. (They're typically rated for 10A/120W or so each, the fact your fuse is 20A leads me to believe that there MIGHT be more than one socket on that circuit)