Merchant Gourmet do pouches of cooked lentils and grains which keep at room temperature until opened. You could buy more than one and mix them.
Alpro do little pots of chocolate soya desserts which in our house are known as gloop. They taste better cold, so I keep them in the fridge, but they don't actually need refrigeration and taste fine eaten at room temperature.
Assorted nuts, or fruit/nut mixture, preferably not salted?
Oatcakes and a jar of tapenade. I don't think that would come to any great harm not being put in the fridge after opening.
I am fairly gung ho about this kind of thing, so in winter would have no qualms about taking a small pot of hummus with me. I think it would be fine out of the fridge unopened for 24 hours or so. Eat with oatcakes, crackers, breadsticks or pitta/flatbread.
A whole carrot would be absolutely fine out of the fridge, if you are OK eating them unpeeled. Carrot sticks in a little sealed tub would probably also keep well out of the fridge for a day or so. I'd be less sure about more watery things like cucumber, peppers and lettuce. Tomatoes would be fine. I don't keep tomatoes in the fridge so know they keep for a while at room temperature. Your main issue there would be transporting them in something that will keep them safe from being squashed.
Soreen malt loaf doesn't need butter (in my opinion). I like the banana version.
If you do take teacakes, I'd split and butter them at home and put them in a box or wrap in clingfilm for transport.