Depending on the University, most are pretty close/accessible to decent shops, such as larger supermarkets, an Argos (within Sainsbury), The Range/Dunelm, and they can also get online orders delivered (supermarkets, Argos, Amazon etc) etc., so don't panic and buy every conceivable item they may ever need in terms of kitchen stuff, storage, etc. All they need to start is the basics - they're not going to be cooking spectacularly complicated meals in the first week or two, and if all they can take with them is one set of bedding, that'll last for the start and they can buy a second set once they're there.
More important are the personal items, clothes, momentos of home/family, laptop/phone chargers!
Also maybe heavier stuff they won't be able to carry back from Argos themselves, i.e. clothes airer, plastic storage shelving system, duvet, etc.
I think it's well accepted that most students take far too much (well the ones who are taken there by parents with big cars anyway!). Lots of stuff is simply never used and comes home again often still boxed, like sandwich toasters, omelette makers etc which your student son/daughter deemed "essential"!
Even in flats with kitchens, students still go out for meals, buy lunches on campus, some even nip down to the university "cafe" for breakfast en-route to lectures. Depends on the campus set up - some have several "on campus" options for cafes, shops, takeaways and city based campuses often have such places pretty close to cater for the students.
All I'm saying is don't think you have to send them off with every conceivable item they (and you) think they'll need. They can buy stuff once there, they can borrow stuff from flatmates. Pointless all flatmates taking their own baking trays for the oven - it probably already has one, and if not, they can work between themselves to decide who buys what to share, i.e. x buys a baking tray, y buys a tin opener, z buys a roll of kitchen foil, a buys a bottle of washing up liquid etc etc.