Ty, the fastest way for gaining cooking exp in f2p is just make money in other skill and buy raw lobbies, then go to falador east bank, having a hatchet equipped and a tindy in your inventory. cut the closest tree to the bank, light it and cook food, Cut the tree again, bank food, go to the tree, light a fire, cook food, cut the tree... .
Do this when you don't burn more than 2 lobs/26.
An interesting fact is, while I was lvl 75 cooking, I would burn 1 lobby in my inventory while cooking on a range, but none when cooking on a fire
lvl 82 ftw! :p
Also, you can gain extra cooking exp while flyfishing at barbarian village, I got this way up to 70 cooking