NiNi_Awesome08 Gaming laptops have gaming-tier hardware, although some high-end non-gaming laptops do as well. (Not in the £800 range though.) That means better performance, and also usually a bulkier chassis to accommodate the more robust cooling that the hardware needs. That hardware will also use more power, often even on idle, so you probably wouldn't get great battery life. And those fans are going to be somewhat loud, at least in this price range.
The right non-gaming laptop could still allow you to use all official Sims 4 content and plenty of mods though. It's just a matter of picking the right configuration. Plus, the processors are generally built to perform regular tasks at a very low power profile, meaning better battery life and quiet to silent fans when you're not running a game.
For gaming laptops that aren't too flashy, what do you think of these?
https://ao.com/product/c17wheaabubun-hp-victus-15fa2300na-laptop-black-109078-251.aspx
https://www.argos.co.uk/product/7806908?clickPR=plp:15:43
The second one is £820, but I'm not seeing a lot of options with an RTX 4050 or (the slightly faster) 5050 that are reasonably subtle. You could drop down to an RTX 3050, but that wouldn't save you much money, maybe none depending on the model, and they're going to look like these. Plus, a 3050 is significantly slower, still more than capable of running Sims 4 on ultra settings but not with the same kind of margin you'd get with the other models.
If you do want a gaming laptop but don't like these two, let me know why and I'll list other options. I do think these fit your preferences the best, at least among those I can see, but you're the one who has to use it.
You have a lot more good options in the non-gaming laptop category, for example these:
https://www.currys.co.uk/products/asus-vivobook-s14-m3407ha-14-laptop-amd-ryzen-7-1-tb-ssd-silver-10286936.html
https://www.currys.co.uk/products/msi-prestige-14-ai-evo-14-laptop-intel-core-ultra-5-512-gb-ssd-grey-10280523.html
https://www.currys.co.uk/products/acer-aspire-14-ai-oled-14-laptop-copilot-pc-intel-core-ultra-5-512-gb-ssd-silver-10284846.html
https://www.currys.co.uk/products/hp-omnibook-7-aero-13.3-laptop-amd-ryzen-ai-7-1-tb-ssd-silver-10281524.html
These are all in the same performance category (can run Sims 4 on high-ultra settings, maybe ultra, without factoring in custom content), although the third is a little faster than the others.
If you want a pretty screen, the third has that too, as does this one that's a bit more expensive and has the same internal hardware:
https://www.currys.co.uk/products/asus-vivobook-s16-oled-s3607ca-16-laptop-pc-intel-core-ultra-5-1-tb-ssd-silver-10284282.html
The fourth of the group above is listed at less than 1 kg, with the third being the next-lightest, but all are 1.7 kg at most, which is reasonable for carrying around.
Let me know what you think of these, and if you want more options in a certain category (for example 1-1.2 kg), I can search other sites too. But there are too many options to cover without narrowing things down.
And if you have more questions, please feel free to ask.