@FatfQker I checked sold items and prices, and it looks like the best laptop configuration typically sold for £200 or less is an Intel i5-1135G7 processor, 8 GB RAM, and 256 GB storage. The processor and its integrated graphics chip can run all current Sims 4 packs together on medium-high or high graphics settings, and the RAM and storage are sufficient for the game.
The only other detail that matters, other than the laptop being in good working condition of course, is that it comes with Windows 10 or 11 already installed. If Windows is in S mode, you can "upgrade" it to Home for free, which is necessary before installing Sims 4.
If you see an option with 16 GB RAM, that would be better, but don't worry too much about it. Similarly, 512 GB storage would be nice to have but isn't necessary if this laptop is just for Sims 4. Between the two, I'd pick more memory over more storage.
Any given processor will always come with the same graphics chip, so you can choose just based on the CPU. Other similar options to the Intel processor are an AMD Ryzen 5 5500U or Ryzen 7 5700U. They're in the same perfornance category as an i5-1135G7. Putting aside the possibility of a defective laptop, any system with one of these three processors should be within a few percentage points of any of the others in performance, so they're all roughly equally good choices as long as they also have at least 8 GB memory, 256 GB storage, and Windows. The i7-1165G7 is a bit faster but isn't a necessary upgrade.
Here's one example that's Buy Now for £190:
https://www.ebay.co.uk/itm/166181273434
If you don't like it for one reason or another, for example the screen is too small or the keyboard isn't quite right, this should give you a list of all options with an i5-1135G7 CPU, sorted by price:
https://www.ebay.co.uk/sch/i.html?_from=R40&_nkw=i5-1135g7&_sacat=177&_sop=15
I'm sure you know how bidding goes on Ebay, so it might take a little time to get the system you want if you don't find one with a Buy Now button, but going by the recently-completed sales, you should be able to get something for around £200 sooner or later.