b52c4653883427fa Unfortunately, there aren't many 17" laptops available at all, at least not in this price range. (There are plenty of these in the high-end gaming laptop category, but I doubt you want to spend an extra £1,000 just for a slightly larger screen.) There are a reasonable number of of 16" options though, including a few I'm listing here that are right on the edge of what's required to run Sims 4 on ultra graphics settings. Again, this would depend on how your wife plays, what extra content she uses (if any), and how smooth she wants the game to be. But a mix of high and ultra settings would likely be more than fine.
These two have the same processor and graphics chip, screens with equivalent brightness and quality, and 16 GB memory. The more expensive one has twice the storage, but that wouldn't be necessary for Sims 4 alone. Still, your wife might have a use case for it.
https://www.argos.co.uk/product/8029368
https://www.argos.co.uk/product/7956470
This one has a newer processor, although not any better as far as Sims 4 is concerned, but its graphics chip is somewhat faster, maybe in the 10-15% range for gaming.
https://ao.com/product/x1607aamb019w-asus-vivobook-16-x1607aamb019w-laptop--silver-111136-251.aspx
There are a few other options along these lines that are a little more expensive, still under £800, but they're not an improvement. So I would consider these three first, and only look for others if you don't like any of them for one reason or another. In that case, let me know what it is about these that doesn't work for you, although like I said, a 17" screen just isn't going to happen in this price range, that is unless you buy a used model, probably on a peer-to-peer site like Ebay.