I have been using, and used to make, an insulated game bag inside my hull for many years. Really is a great way to go, keeps the inside of your kayak clean and keeps the fish nice and cold when combined with some ice packs. For the ice packs I use a couple of different things,
Techni-ice is sheets of material that absorb water, you freeze these sheets and lay inside the bag. I prefer this method over bottles of water because they form to the contour of your kayak and you can lay them directly over the fish. Just refreeze them at the end of the day. Before first use of these sheets I soak and freeze them then vacuum pack them so that they don't absorb the blood and slime from the fish, this will keep them from getting really stinky.
Another option to the Techni-ice is to do the same thing with a diaper. Soak it with water then freeze and vacuum pack, this is a much cheaper way to go and does work.