@Amadiora While 256 GB is enough for Sims 4 and all its content, plus plenty of other small apps like browsers, it may not be enough if you want to install another large game, or if you have a significant amount of data you want to store internally. Of course, for £550, you could get a large external hard drive for overflow and still stay around your max budget. Applications run more slowly on external drives, but they're fine for data like photos or music.
By the way, there's a 512 GB Acer with a 4500U, but it's currently sold out at Currys (normally £550). If you're curious:
https://www.currys.co.uk/gbuk/computing/laptops/laptops/acer-aspire-5-a515-44-15-6-laptop-amd-ryzen-5-512-gb-ssd-black-10208163-pdt.html
And these two are nother options with a 4500U and a 256 GB SSD, but for £500, they're worth considering if the hard drive size is okay with you.
https://store.hp.com/UKStore/Merch/Product.aspx?id=1E6Z9EA&opt=ABU&sel=NTB
https://www.argos.co.uk/product/8114448
For £600 or a bit more though, you could get a an entry-level gaming laptop with a graphics card capable of running all current Sims 4 packs on ultra settings. I'm not sure whether you want a laptop that size, but here are a couple examples, both with a 256 GB SSD.
https://www.laptopsdirect.co.uk/acer-aspire-7-ryzen-5-3550h-8gb-256gb-ssd-geforce-gtx-1650-15.6-inch-window-nh.q8lek.001/version.asp
https://www.currys.co.uk/gbuk/computing/laptops/laptops/acer-nitro-5-15-6-gaming-laptop-amd-ryzen-5-gtx-1650-256-gb-ssd-10205931-pdt.html
I couldn't find a laptop with a 1650 and a 512 GB SSD for less than £700 though. It doesn't mean they don't exist, just maybe that they're not in stock right now, or the price has gone up.
https://www.argos.co.uk/product/9199527
If you don't want a bulky gaming laptop (although the Acer Aspire is listed at 2.15 kg), this Asus would be a good compromise. It's £600 and has an Nvidia MX250, a dedicated card that's slower than the 1650 but still faster than the chip in a 4500U. This laptop also has a 512 GB SSD, and it weighs 1.5 kg.
https://uk.store.asus.com/laptops/vivobook-series/asus-vivobook-red-a412fl-ek378t-14-full-hd-display-mamoedge-screen-laptop-intel-core-i5-8265u-processor-8gb-ram-512b-ssd-winndows-10-screenpadtm-2-0.html
If you have more questions about any of this, please feel free to ask.