Laptop

rachk116  The single most important component here is the graphics card or chip, and in your price range, you're looking at an integrated graphics chip, as in, integrated into the processor.  (Laptops with dedicated cards typically start around £700.)  So the key is to pick a laptop with a processor that has a fast-enough graphics chip.

The next-most-helpful detail is getting 16 GB RAM rather than 8, which is doable in your price range but cuts down on the options.  This is important because the graphics chip borrows from RAM to do its processing.  That 8 GB RAM can become 5 GB available once Windows takes its share, then 3-3.5 when the iGPU is borrowing significantly, as it would when running Sims 4.  That's enough for the game most of the time, but not much else.  With 16 GB installed, it's not an issue.

Anyway, here are some suggestions that meet the criteria.  Their graphics chips should be able to run all current Sims 4 packs together on medium-high to high graphics settings.

https://www.currys.co.uk/products/acer-aspire-3-15.6-laptop-intel-core-i5-512-gb-ssd-silver-10254475.html
https://www.currys.co.uk/products/msi-prestige-14-evo-14-laptop-intel-core-i5-512-gb-ssd-silver-10267081.html
https://www.argos.co.uk/product/7144677
https://www.dell.com/en-uk/shop/laptops-2-in-1-pcs/inspiron-15-laptop/spd/inspiron-15-3520-laptop/cn32042sc?ref=variantstack
https://ao.com/product/m1502yanj033w-asus-vivobook-15-laptop-silver-102044-251.aspx

The second one has the best screen by a significant margin, especially if you plan on playing in a brightly-lit room.  The graphics chip in the third and fifth is a bit faster than the others, not a whole category faster but maybe something like 10%.  Aside from that, they're all similar enough; choose based on whatever details matter to you, whether screen size or keyboard or aesthetics.