At this price, and with uni as a focus, I would be prioritising good battery life, portability, screen, silent running and productivity over gaming. Also cheaper gaming laptops often require the proprietary power supply and won't always charge from USB C power banks etc.
If Gaming then:
Something like an ASUS TUF Gaming A15 15.6" Gaming Laptop - AMD Ryzen 7, RTX 3060, 512 GB SSD @£799
The reason I like the TUF gaming laptops at the cheaper end is when not gaming, on the right models you do get decent battery life still.
There are various TUF options from £650-£1000 and even the i5/r5 CPU versions are fine if you get the 16gb Ram versions.
A RTX4050 or RTX3060 is all you need.
A alternative would be HP Victus 15.6in i5 16GB 512GB RTX4050 Gaming Laptop @£849
However, a 1.2kg laptop vs 2.4kg makes a significant difference though so I would pick something like
An ACER Swift Go 14" Laptop - Intel® Core™ i7 (13700), 16gb RAM, 512 GB SSD, Silver @£699 which weighs 1.2kg has a touch screen and Thunderbolt 4.
Or the ASUS Zenbook 14 UX3402VA 14" Laptop – Intel® Core™ i5 (1340p), 16GB RAM, 512 GB SSD, Blue @£799 which has an epic oled 2.8k screen.
Integrated graphics will still run Minecraft / Roblox etc fine.
For more serious gaming, a mid tier Geforce Now subscription is the way forward.