Which laptop should I buy for under for £1000 - for university and light gaming?

I want a laptop for under £1000 that is good for university. It should be able to cope with games like Runescape, Sims, TF2, Overwatch, Minecraft (I don't play all of these - just examples lol). It should have a decent battery life, enough space for a few games as well as many documents, and also it should last a relatively long time (I'm not starting uni till next year). Not too keen on Macbooks and not bothered about having a touch screen.

I've researched a bit and I think the one I'm most keen on at the moment is the ASUS ZenBook UX330UA. I wish I could get the Dell XPS 13 but it's too expensive! I'm a bit confused though, because on Amazon there are two versions of this ASUS laptop: FB100T and FC093T - what's the difference? One of them is £100 cheaper and I don't want to spend an extra £100 if it isn't needed.

Here are the links to the two of them. Is the £100 more one more expensive because of it's i7 intel core instead of i5 intel core? Honestly, I hate all these numbers and words I don't understand properly lol despite doing a bit of research.

https://www.amazon.co.uk/...B01MU9LRV9
https://www.amazon.co.uk/...073Q48Y3Z/

So does anyone else think this ASUS Zenbook would be good? Or has anyone got any other ideas?

You don't get the battery life, but performance is very high on this MSI
https://www.saveonlaptops.co.uk/9S7-14A112-090-MSI-GS40-6QE(Phantom)-090UK_1945621.html
60 fps OVERWATCH Ultra Preset average performance expected on AC power.
cpu benchmarking
https://www.cpubenchmark.net/...u_list.php

And this is probably the right choice pushing the battery life to about 4 hours average.
https://www.saveonlaptops.co.uk/UX430UQ-GV048T-ASUS-Zenbook-UX430UQ-GV048T_2108569.html
Overwatch medium-high on AC power is smooth.
ASUS Zenbook UX430UQ-GV048T
i7-7500U, 14" Full HD 1920x1080 Screen, Windows 10 Home 64-bit, 8GB DDR4 RAM, 512GB SSD, Dedicated GeForce GT 940MX 2GB DDR3 Graphics, Bluetooth 4.1, 1x USB 2, 1x USB 3.0, 1x USB 3.0 Type C, Backlit Keyboard, 5-6 Hours (Upto 5 Hour Battery Life) (This means 4 hour battery life), 1.3 Kg

This is graphics processor to gaming:
https://www.notebookcheck.net/...849.0.html
In 7th gen core i, integrated Intel is HD 620 is rank 299 on the table. On battery, it also cuts it back a little more.
1920x1080 resolution also lowers the fps. Overwatch should play on low settings on i5 or i7 U suffix dual core 7th gen Intel.

1TB HDD or 128GB SSD are £43, 256GB SSD is £78, 512GB SSD is £139

ASUS ZenBook UX330UA-FB100T £890 3200 x 1800 13.3 display will reduce gaming performance in half.
£860 instead:
https://www.saveonlaptops.co.uk/UX330UA-FB100T-ASUS-Zenbook-UX330UA-FB100T_2063859.html
UX430UQ-GV048T minus the GTX 940MX and change display from 14.1 1920x1080 to 13.3 3200x1800 and reduce price £140

ASUS UX330UA-FC093T £800 Amazon, 1920x1080, i5-7200U
cpu is 10% reduced. The difference between i5-7200U and i7-7500U is only clock speed and CPU cache.
The display is cheaper as 1920x1080.

https://www.saveonlaptops.co.uk/80V00042UK-Lenovo-IdeaPad-510S-13IKB_2072640.html
A 13.3, 1920x1080, 1tb hdd with i5-7200U is only £499
You can buy a 512 SSD and enclosure for £160 and clone and swap to have an external 1TB and internal 512SSD at £660

Nice Thinkpad at £735 gets a business level laptop
https://www.saveonlaptops.co.uk/20J1000JUK-Lenovo-ThinkPad-13_2085416.html

You pay a premium in a below 15.6 inch.
This one is interesting if gaming is not important
https://www.saveonlaptops.co.uk/XPS9250-0939BLK-Dell-XPS-12-9250_2000964.html
Audio is an issue
https://www.notebookcheck.net/...679.0.html

There are nice laptops in a 15.6" that cost less, but since looking at 13.3, I think 14.1 is better at college but both are more portable than 15.6.