sarahrory This is the best laptop I'm seeing for £400 or less:
https://ao.com/product/bh3g3eaabu-hp-omnibook-5-laptop-silver-110180-251.aspx
It's the only new model I found with 16 GB RAM (and otherwise decent hardware), which is a significant advantage when you're dealing with integrated graphics, even if having 8 GB isn't fatal. Its graphics chip is also faster than anything else I'm seeing in this price range. It should be capable of running Sims 4, all current packs included, on high graphics settings, possibly with one or two turned down to medium.
If you don't like that one for whatever reason, this is the next-best model I found, with a graphics chip that's not as fast as the one in the laptop above but should still be able to handle medium-high settings:
https://www.argos.co.uk/product/7788507?clickPR=plp:20:229
If neither is what you want, let me know why, and I'll have another look. There are other options for the same price that are good enough, just not as good as these two.
And if you have more questions, please feel free to ask.