Simswhynotplay If you don't mind your laptop running loud and hot—not dangerously so, just enough to get the fans going—this is a good cheap option. It can handle all current Sims 4 content on ultra graphics settings with some room to spare and is the cheapest new gaming laptop I'm finding right now.
https://www.currys.co.uk/products/msi-cyborg-15-15.6-gaming-laptop-intel-core-i5-rtx-2050-512-gb-ssd-10266064.html
These have an RTX 2050 graphics card, which is slower than a 3050 but still likely capable of ultra graphics settings as long as you don't pile on the high poly custom content. They're about the same in terms of overall build quality: not high-end but also not two years away from being unusable.
https://www.laptopoutlet.co.uk/lenovo-loq-15iax9e-i5-83lk002suk.html
https://www.laptopoutlet.co.uk/asus-tuf-gaming-amd-fa506nf-hn008w.html
These are the next-cheapest laptops I'm seeing with an RTX 3050 that are reasonably-good, with the Alienware being a high-end laptop that usually doesn't even come with cheaper components like this.
https://www.currys.co.uk/products/acer-nitro-v15-15.6-gaming-laptop-amd-ryzen-5-rtx-3050-512-gb-ssd-10265657.html
https://www.dell.com/en-uk/shop/gaming-and-games/alienware-16-aurora-gaming-laptop/spd/alienware-aurora-ac16250-gaming-laptop
I haven't found other options with a 3050 for less than £750, but I also couldn't load the Argos website (down for maintenance) or the HP shop site (endless loading, both the site overall and your link that previously worked for me) tonight. I'll check back later if you don't want any of these laptops. But you can also check yourself if you like. For Argos, choose the Gaming Laptop category, filter by price low to high, and look for an RTX 3050, or a 2050 if necessary, not from Medion and not an HP with an Intel processor. For the HP site, look for a 3050 or 2050 with an AMD processor; these don't have the same issue.
I can also check back in a day or two if you want.
And if you have more questions in general, please feel free to ask.
Edit: The Argos site is loading for me now, and I found two more options worth mentioning. This one has an RTX 3050 and is £680:
https://www.argos.co.uk/product/7575521
And this one has the newer and somewhat faster (unnecessary, but nice to have if it's in your budget) RTX 4050, although still in the noisy MSI chassis:
https://www.argos.co.uk/product/4375834
I would definitely get the Asus from Argos over the options with an RTX 2050 due to the significant improvement in performance, but I'm leaving those other links up in case you or someone else has already read the post and might wonder where they'd gone.
The HP site loaded too, after a delay, but only has two gaming laptops in your budget, both with Intel processors and not as cheap as the Argos options or the MSI from Currys. So it would be best to skip the HP options entirely.