What's the cheap compass that you have? In my experience, some are okay, and some are not so good (difference between cheap and cheerful and cheap and nasty). A Silva style one with a liquid filled capsule should be fine - decent size to be easy to read, and will survive a soaking.
You might want to consider some other kind of pot if you're going to use a fire - the billy can type can be dangled above the fire and the handle is kept out of the flames. You can also set things up such that you can regulate the heat that the pot gets. With mess tins, you have to keep them at the edge of the fire and you need to ensure there's some sort of support to keep it level. They also don't have a lid, which means longer boiling/cooking time and a greater likelihood of bits getting in.
I haven't used hexi for many years, but my recollection is that they aren't very good (slow and messy is what I remember). A small gas thing is much better - the little 'rocket' types that screw into the top of the canister are small and light, but the canisters can be a bit of a pain if you need a bigger one, while the small ones are relatively expensive for the amount of gas that you get. The ones that have a tube between the burner and canister are more stable but a little bit bigger. Very handy for a quick brew and as a backup for cooking if a fire isn't an option. Wind can be an issue at times - find a sheltered spot or sort out a windshield.
Consider extracting the useful bits out of the first aid kit and putting them into a pouch, or get a new one. The LifeSystems ones are okay - compact and have waterproof zips. The Pocket or Trek are pretty cheap (£10-12), almost to the extent that the pouch alone is worth the money, and cover the main things (cuts, lacerations, blisters, pain). Add/remove bits as you see fit.
The little keychain torch might be okay for getting things out of the rucksack, but it might not be up to helping you to navigate in the dark, should that become necessary. I got one of these recently:
http://www.maplin.co.uk/p/cree-technology-flare-led-torch-a76kf It's bright enough to get around in the dark, adjustable from flood to spot (very handy) and also has adjustable brightness (press and hold the button to ramp the brightness down). I would say the usable battery life is a bit shorter than the stated 3 hours - 2 is more realistic, so a spare or two is a good idea.
If you prefer boots in rougher terrain, I'd consider getting them sooner rather than later. In woodland, shoes might be okay on the paths, but it can get rough very quickly as soon as you get off the path, which is where firewood and campsites tend to be. Boots also handle puddles and shallow streams much better and tend to stay on if you go ankle deep in mud. I like the high-leg combat type boots.
I would strongly recommend getting a sleeping mat. As mentioned already, you might not have the option to use foliage, not only due to the permission aspect, but because something suitable might not be available (or everything might be soaking wet). There is also an ecological side to it - it's fine to be out in the woods enjoying oneself, but we need to be mindful of not damaging the environment unnecessarily just to please our backwoods sensibilities. There is a balance to find with this sort of thing.
A pair of leather work gloves can be a good idea. Sometimes, it's just better to protect your hands if rough handling is needed, and they're good for dealing with pots and fires. The all-leather yellow/tan ones in DIY places and garden centres are good - decent protection and still retain good feel.
You might find that the rucksacks you have are too small for the overnight stuff. Do some trial packs at home when you get the other bits and see how things go. They should be fine for a day's bimble.
Apropos the Fenna list (I'm sure Ray Mears has something similar in one his books, as well), don't forget a little luxury or two to occupy yourself with once the camp stuff is done. For me, that would be binoculars, and a pipe and baccy (something to wander about with, and something to sit and do nothing with).
As already said by others, you have just about enough to be getting on with for a day out at least (need a water bottle and cup). Kit choices are nearly always influenced by experience - a lot of it is about trying to make things function better, or with less hassle, and using the stuff informs that better than anything else. Aside from the water bottle and cup, if I were to pick one thing that you don't have yet, even for a day out, that I would consider essential, it would be boots.
