It's looking like a Windows 10 laptop then, an i3 8th gen CPU U or Y model with 8gb ram, something by Lenovo HP Acer Asus. They'll be rock solid.
Also look for grade A returns you can get a better laptop at a reduced price. Laptopsdirect does some very good deals.
Overall they are all pretty much similar at a £400 price point youd be hard pressed to get 16gb ram and a 1tb ssd.
If you want a Mac then you'll be looking at a second hand 5yo at around £500, even the newest cheapest one are nearly a grand.
Don't get anything with a celeron processor they end up chugging after a while, Look to see if it has an i3, i5 or if your lucky i7.
The speed is not that important for CPUs the GHz bit. you only need to care about that if your playing higher end games or doing a render in a video editor.
Battery life is very dependent on what your doing with the laptop it's screen brightness that's eats most if the battery.
At your price point see if you can get USB-c charging it means in practical terms you can use many powerbricks as a lot if the power jack's are proprietary and if you loose the brick they can be a pain in the arse to find a comparable one.
Is weight an issue? as 15 or 17 inch screen laptops can be quite hefty to lug to school. The sweetspot is13 inch, lower than that it gets a bit squinty.
Touchscreen as well can be a bit meh! in laptops nothing more annoying than someone leaning over your shoulder and dicking around with what your doing.