As a lifelong angler I knew exactly what I wanted in my kit when I made it up. A 100m spool of 4lb nylon monofilament has oodles of extra room on it for more line, so I added about 20yds of 12lb line on top and then another 20yds or so of 20lb line on top of that. By carefully removing the little strengthening vanes and the spindle tube from the inside of the plastic spool I was then able to push-fit a little plastic container inside the spool. This container is what spare split shot comes in from the tackle shop (I bought BB's for my kit). In with the BB's are 2 or 3 small ledger weights, 10 size 14 hooks (Eyed, Made by Mustad) 10 size 8 hooks the same and 10 size 4's the same again.
All these fit in the pot the split shot came in with the shot, and the pot them wedges snuggly into the inside of the spool, so the whole kit only takes up the space of a spool of line. With this set up I have plenty of line to use for binding/whipping any items I want to make, and for setting "alarm tripwires" around camp if I feel the need. (As many in the Southern States have recently discovered; In a survival situation not all "visitors" are particularly welcome)
I don't carry floats at all. Anyone with a knife can very quickly make usable floats from twigs or waterside reeds if they want them. A rod (pole) can be of any long stick if you want one, or simply fish hand-line style.
With a little finesse in your approach to the water there is no need to fish "ultra-fine" to get bites from most coarse fish if you bait up with the appropriate tasty morsel. Perch, if big enough, are in my opnion better eating than trout, and are absolute suckers for a nice wriggly lob worm ledgered hard on the bottom.
Roach are not that much of an eating species, but can be caught on maggots, bread (and similar stuff) as well as grains of soaked wheat or corn and elderberries.
Eels simply love worms. In a survival situation a nightline baited with a couple of lob worms on a hook as big as a #4 to line as heavy as 12lb is very unlikely to be empty in the morning if there are any numbers of eels present in the water.
Although I am a keen pike angler I would probably advise most folks from avoiding them if possible. They have razor-sharp teeth (over 700 of them) and bite through nylon line effortlessly. These predators will "steal" fish from your nightlines by biting through the line, so unless you have a steel trace (Hook length) you are unlikely to land them.
Set lines, nightlines, nets and any other method of fishing in fresh water where you are not present and able to attend to the captured fish immediately, are all illegal in the UK so practice with these methods is not an option unless you are willing to sit by your tackle and "deal" with fish as they take the bait. (To comply with the law you also need a Rod Licence available from the Post Office, and the permission to fish from whoever owns the fishing rights on the water) As has been said before, in a true survival situation the rules on these matters would go out of the window as far as I am concerned. In such a true emergency situation it might be worth bearing in mind that your proximity to any town will ensure that ducks and even swans are likely to gather at your feet if you start throwing little bits of anything white that floats onto the water, and we all know how to cut a long stick don't we boys and girls.....
Edit to add that spear fishing and bow fishing are also illegal in fresh water in the UK, but same rules apply as above if your life is on the line.