@KitKezzle The single most important component in determining how well a given computer will run Sims 4 (and most games) is the graphics card. In the £500 and under range, there aren't any dedicated cards available, only integrated graphics chips, and the fastest ones are in AMD Ryzen 5 or 7 processors. These chips can run the game on medium settings, or maybe medium-high if you only install a few packs. The chip in the one you linked is fine too, it's just not quite as fast.
On that note, these laptops (£421-450) all have the same hardware: processor, graphics chip, memory, and storage. Their hard drive is small though, only 256 GB. That's more than enough for Sims 4 and all associated content, plus plenty of small apps like browsers. But if you plan on storing a lot mroe data, it might not be enough. (If you're not sure, check how much storage you're using on your current computer for comparison.) Having a solid state drive (SSD) will improve overall performance though, with everything from Windows to many apps loading a lot faster, so the tradeoff is usually worth it.
https://www.laptopoutlet.co.uk/lenovo-v15-ada-15-6-full-hd-laptop-amd-ryzen-5-3500u-8gb-ram-256gb-ssd-windows-10-iron-grey-82c70005uk.html?___SID=U
https://www.box.co.uk/M509DA-EJ034T-ASUS-M509DA-EJ034T_2961552.html
https://www.currys.co.uk/gbuk/computing/laptops/laptops/acer-aspire-3-a314-22-14-laptop-amd-ryzen-5-256-gb-ssd-black-10209211-pdt.html
If you need more storage, these two are a bit more expensive, but they have a 512 GB SSD instead, and otherwise the same hardware as the ones above.
https://www.laptopoutlet.co.uk/hp-255-g7-15-6-full-hd-laptop-amd-ryzen-5-3500u-8gb-ram-512gb-ssd-windows-10-1b7k2es-abu.html?___SID=U
https://uk.store.asus.com/laptops/vivobook-series/asus-vivobook-red-x512da-ej142t-15-6-full-hd-nanoedge-display-laptop-amd-ryzen-5-3500u-processor-8gb-ram-512b-ssd-windows-10-includes-backpack-case.html
This HP is £500 and has a small SSD, but its processor is somewhat stronger and its graphics chip somewhat faster than the ones above. It's really just the new generation's version of the other laptops, but this generation's hardware is an improvement over last year's.
https://store.hp.com/UKStore/Merch/Product.aspx?id=1E6Z9EA&opt=ABU&sel=NTB
Aside from the last laptop, performance should be quite similar with all these models, so you could pick the one you liked the best among them and not worry about the specs. If you have questions about any of this, please feel free to ask.
