nicolagreene The single most important component in determining how fast a given computer will run Sims 4 is the GPU. For £500, you're not going to find a laptop with a dedicated graphics card, at least not outside of a really good Black Friday deal. So you're looking at high-end integrated graphics.
The next-most-important detail is the memory: you'll want 16 GB RAM since the iGPU will borrow some for graphics processing. That cuts down significantly on your options, since most laptops in your price range have less memory, but there are still plenty of good laptops available.
Among the systems with 16 GB RAM, this laptop (the £450 model with the Ryzen 5 7530U, not the base £430 model) has the fastest graphics chip I'm seeing for less than £500. It should run all current Sims 4 packs together on medium-high to high graphics settings:
https://www.dell.com/en-uk/shop/laptops-2-in-1-pcs/dell-15-laptop/spd/dell-dc15255-laptop
For £500, this one is significantly faster—you might be able to play on ultra settings:
https://www.currys.co.uk/products/msi-prestige-14-ai-evo-14-laptop-intel-core-ultra-5-512-gb-ssd-grey-10280523.html
This one is also £500 and its graphics chip is somewhat slower than the one in the MSI above but a lot faster (maybe twice as fast in gaming) than the one in the Dell. It should handle some combination of high-ultra graphics just fine.
https://www.currys.co.uk/products/acer-aspire-15-15.6-laptop-amd-ryzen-5-512-gb-ssd-grey-10284831.html
So if you are willing to spend the full £500, I think the upgrade in graphics processing power is well worth it. But you don't absolutely have to in order to play with good performance and decent graphics.
If you have more questions, please feel free to ask.
