@chloejmc The MSI Cyborg isn't a terrible laptop, in that it won't fall apart on you the day the warranty runs out. But yes, you can do better in terms of one or more markers of quality: noise, heat, screen, feel under your fingers, etc. For example, this one runs cooler and quieter and has a better screen:
https://ao.com/product/fa506ncrhn016w-asus-laptop-black-103047-251.aspx
This one is a good alternative, even under £600 with an e-voucher. It does only have 8 GB RAM, but you could upgrade it yourself (memory is cheap and easy to install) and still stay well within budget. It's also not strictly necessary just for Sims 4, at least not with a gaming laptop, because the graphics card has its own VRAM that it will use rather than borrowing from main memory.
https://www.hp.com/gb-en/shop/product.aspx?id=6P0W4EA&opt=ABU&sel=NTB
You could also get basically the same Asus as above except with 8 GB RAM and an RTX 4050. The extra power is also not necessary for Sims 4, but you can't upgrade the GPU after the fact. To be clear, an RTX 3050 should always be able to handle Sims 4 on ultra graphics settings, unless the game changes significantly in a way that hasn't been indicated so far. This is more about the possibility of other games, or high poly custom content, or ReShade, or whatever else you might want to add in the future.
https://www.overclockers.co.uk/asus-tuf-gaming-a15-nvidia-rtx-4050-8gb-15.6-fhd-amd-ryzen-5-7535hs-lapt-lap-asu-03776.html
I'm not seeing anything else as good for under £700 right now, which is unsurprising given that most of the holiday sales are over.
Personally, I think the Asus is better than the HP, considering all the details of the two laptops. But it's not so much better that it would be worth stretching your budget, and it's questionable whether it's worth the extra £80-90 it would cost after you added in the price of more RAM for the HP (if you decided to go that route). On the other hand, if you're not going to upgrade on your own, it would be great to have the extra memory for the future.
If you have more questions, please feel free to ask.