Ahem i got my expedition badge from cadets :P
It depends on what facilities will be available to you and of course it's in June but you still need warm clothes incase the weather isn't great. But you'll be around civilisation.
Enough clothes (including bad weather gear), enough food and drink or money to buy more if that's your plan. Plus cutlery, dishes and plates or even better those army style sets or tins, maybe a camping stove if you're doing your own food. Bottles for storing water if you can fill them up. A swiss army knife or one of those other little tools thats ten things on one etc.
Tent, fly sheet (most decent tents have one attached) roll mat or blow up bed (remember a pump if you're going for this option), sleeping bags or blankets. Sleeping bags come in different thicknesses and if it's a warm night and you have a thick one, you'll be sweating like a pig.
Torches, spare batteries, first aid kit, spare tent pegs if available, a hammer/mallet, sun hat, sun cream, toilletries (and toilet paper).
That's all I can think of ATM.