I had this identical problem, and I too wish I got to it sooner than I did before it got quite big. My problem was about the same width as in the picture but lower down and underneath a bit.
I ended up grinding the surface down to bare metal to uncover how far the rust spread, then literally pulled all the rusted metal away just with my hands until it got tougher, then cut away with a dremel a little further beyond the rusted metal to make sure I got everything. I painted it with kurust just incase, then cut a new piece of metal larger than the size of the hole that I cut into the sill. Drilled a hole in the centre of the new piece of metal and screwed in a self tapper so that I could use that as a handle and (very fiddly) angle it and slide it inside the sill through the hole. I then took it to a garage and got it welded for £20 (you have to remove ALL rust otherwise when they weld it will just chase it further and further and wont be a clean edge, nor will your cut piece of metal fit anymore). All I did then was angle grind the weld joints flat and flush with the body, fill it with P38 body filler, Sand, Prime, sprayed stone guard underneath (the soft protection paint), Colour matched spray paint over the top then lacquer on the top of that and looks brand new. I plan on spraying water proofing wax on the inside of the sill through a hole ill make in the rear wheel arch to protect it further in the future.
Sounds like a lot but overall it took me about 10 hours and cost about £50 so cant complain.
