@kirstey08 There are lots of laptops for under £500 that would run Sims 4 (the standard version) quite well. You may not be able to play on ultra graphics settings, especially if you install most or all expansion packs, but medium-high or high settings should be fine. For example, this laptop is £450:
https://www.hp.com/gb-en/shop/product.aspx?id=30A26EA&opt=ABU&sel=NTB
These laptops all have the same or equivalent hardware and should have roughly equivalent performance, plus or minus a few percentage points. However, they only have half the storage, still enough for Sims 4 and all the custom content you could ever download, but not necessarily enough for storing a large amount of data. Still, if you don't like the one above for whatever reason, these are perfectly viable alternatives.
https://www.currys.co.uk/products/hp-14sdq2512na-14-laptop-intel-core-i5-256-gb-ssd-silver-10222231.html
https://www.currys.co.uk/products/asus-vivobook-m515ua-15.6-laptop-amd-ryzen-5-256-gb-ssd-silver-10230027.html
https://www.currys.co.uk/products/dell-inspiron-14-5415-14-laptop-amd-ryzen-5-256-gb-ssd-silver-10230731.html
https://www.argos.co.uk/product/9527584?clickPR=plp:76:96
These two are £500 and have slightly better processors and graphics chips, which means performance should be a bit better. They also have 512 GB storage like the first one.
https://www.currys.co.uk/products/lenovo-ideapad-3i-14-laptop-intel-core-i7-512-gb-ssd-blue-10228904.html
https://www.hp.com/gb-en/shop/product.aspx?id=4H2A8EA&opt=ABU&sel=NTB
Since all of these laptops are in the same overall category, it's totally reasonable to pick the one you like best based on whatever other criteria matter to you. Whichever one you choose, Sims 4 should run very well.
If you have more questions, please feel free to ask.