@MrsLaurenPotts This laptop should handle Sims 4, all current packs included, on ultra graphics settings just fine. It's also nice if not strictly necessary to have 16 GB RAM. If you like it, go ahead and get it.
Otherwise, £800 is definitely a reasonable goal, if somewhat restrictive. I checked a number of different sites, and this is the only laptop I found with equivalent hardware to the one you listed. The RTX 3060 is about as fast as the 4050, the processors are both more than powerful enough to keep up with the GPUs (the one you found is a little better, but the extra power will be lost on Sims 4), and they have the same RAM and storage.
https://www.box.co.uk/82S900Y6UK-Lenovo-IdeaPad-Gaming-3-Intel-Core-i5-16_4378169.html
The next-closest in price with the same hardware is this one:
https://www.hp.com/gb-en/shop/product.aspx?id=800R5EA&opt=ABU&sel=NTB
If you want to save money and drop down to a 3050, there are plenty of options available. But you wouldn't save much money unless you also went with 8 GB RAM instead of 16. While that's fine, Sims 4 doesn't technically need more than that, it's very convenient to have 16 GB. And while you can almost always upgrade a gaming laptop's memory, if you don't want to do it yourself, paying someone else to do it pushes the price back into the 3060/4050 range. Still, if you'd like to see another option, here's the cheapest good one I saw:
https://www.currys.co.uk/products/lenovo-ideapad-gaming-3-15.6-gaming-laptop-amd-ryzen-5-rtx-3050-512-gb-ssd-10249077.html
If you have more questoins, please feel free to ask.
