If they are in halls then there is not a lot of kitchen cabinet space. Usually 1 wall cabinet and 1 base cabinet for all kitchen items plus food, oil, spices, cutlery, utensils, cling film, foil, sandwich bags, chopping board, oven tray, oven gloves, microwaveable Sistema bowl for heating soup etc and a spongematic sponge with washing up liquid in the handle. Ds has a mug this lives in. Ds's halls were fairly new and the cupboards were not 60cm wide ones, more like 50cm same with the fridges where they get one shelf and one freezer drawer.
The best advice I can give is to go into each room and work out what they use in that room, ie their bedroom and look at what they use now, duvet, pillow, duvet cover, sheet, add a mattress topper if they don't already have one. What else do they have in that room? Toiletries? What are they, list them. A desk? Add things under different headings. Bathroom, same things, towel, hand towel, nail clippers, razor, toothbrush, shampoo etc. Same for the kitchen, don't forget medicine, plasters, paracetamol, throat stuff because Freshers' flu is them mixing with germs from all over.
@tribpot your list is great. Ds has 1 pan with a draining lid from Lakeland so good for pasta or veg as no sieve/colander needed, lots cook microwave rice, yes it isn't the best but needs must. Ds cooks from scratch as best he can. He has 1 frying pan, that 1 saucepan, 2 dinner plates, 1 pasta bowl, 1 cereal bowl, 1 cup, 2 glasses, 2 forks, 2 knives etc. He washes up immediately, dries it and puts it back into his lockable cupboard. When you see how other students live you will see why.
Also check YouTube, lots of students upload their room tour which might cover your child's uni accommodation too.