@smizeH2T Memory and storage both matter very much up to a point, but they're more an either/or scenario: either you have enough of each and don't need to worry, or you don't, and you see performance issues. 8 GB RAM is enough for both Sims games, unless you like to heavily multitask while playing, but computers with 16 GB tend to be significantly more expensive. Besides, most laptops in your price range have room for a memory upgrade, and another 8 GB might cost £30.
As far as storage goes, Sims 3 and Sims 4 together take up less than 100 GB, so a 256 GB hard drive would technically be enough. Where it gets tricky is if you like using custom content—I've heard of people downloading 50+ GB of Sims 4 cc. (Sims 3 pretty much grinds to a halt above 10-15 GB cc, depending on the computer involved.) Sims 4 saves are relatively small, but Sims 3 saves can take up a lot of storage, so keeping a large number of backups could theoretically be an issue. And of course keeping a few backups is critical, since saves can get corrupted seemingly without notice. Still, if you're not worried about custom content, or you have an external drive you could use for backups, 256 GB should be fine.
The processor does matter to both games, but not as much as the graphics card or chip, which will almost always be the limiting factor. For Sims 4 as long as you don't get a laptop with an extremely weak processor, you can just consider the GPU. Sims 3 is a bit pickier because it only uses two CPU cores or threads, so overall benchmarks are not as useful—it doesn't help to know what kind of load a 4-core, 8-thread CPU can do if the game can only use a fraction of that processing power.
Anyway, given your budget, the best options available have an AMD 4500U processor, which is incidentally somewhat stronger than the processor in the laptop you've linked. More importantly though, its graphics chip is almost twice as fast in gaming, which would mean raising a couple of settings in Sims 4 or being able to successfully run a couple more expansions in Sims 3. I still think playing with Pets (in Sims 3) might not work out well, and you might have to disable rain and snow in Seasons. But the extra power should definitely help both games.
These laptops all have a 4500U; the last has a 512 GB hard drive. The first two are the same, just from different stores.
https://store.hp.com/UKStore/Merch/Product.aspx?id=1E6Z9EA&opt=ABU&sel=NTB
https://www.currys.co.uk/gbuk/computing/laptops/laptops/hp-15s-eq1510sa-15-6-laptop-amd-ryzen-5-256-gb-ssd-silver-10207935-pdt.html
https://www.currys.co.uk/gbuk/computing/laptops/laptops/lenovo-ideapad-5-14-laptop-amd-ryzen-5-256-gb-ssd-platinum-grey-10208021-pdt.html
https://www.argos.co.uk/product/9188916
The Lenovo comes with Windows 10 S, meaning you'd have to "upgrade" to the Home version to be able to install apps from outside the Microsoft Store, but that's simple and free.
As an example of a laptop with an entry-level dedicated graphics card, this laptop is just under £550 used ("like new"), although new models with this kind of card are a bit more expensive. It's still not capable of running either game on ultra graphics settings, but it's over 50% faster in gaming than the chip in the 4500U.
https://www.amazon.co.uk/ASUS-VivoBook-i5-1035G1-Graphics-NumberPad/dp/B089WBHH3Z/
If you have more questions, please feel free to ask.