I just hit myself up with a HP Stream recently. It has been working really well for me so far and is a good size when lugging it around at 14", because I travel in and out of the local city quite frequently for the library. However, its cons are also its pros for me: essentially, it barely manages anything besides the internet and my Microsoft programs, so it really keeps me on track because I can't piss about on my Steam games (although Terraria and Stardew Valley work perfectly for me) or anything else. In addition to that, it has a good screen, comes with a one year free Microsoft Office: Personal membership, decent speakers and is only £179 at the moment. However, I say this as someone with a backup laptop for my games, Discord, Photoshop, and heavier programs. It all depends on what programs you are using the laptop for at University.
Are you using it solely for Microsoft Office or similar programs? Do you need it to manage games as a past time? Etc?