emilyjh11 Since, as noted, desktops will outperform laptops at the same price point, a desktop is the better option when performance is the priority, or when someone is interested in upgrading. But laptops have obvious advantages too, so this is more a question of what works best for you.
I have a laptop I use for everyday tasks and some gaming, and I have a gaming desktop for long play sessions and anything demanding. I do like to sit in bed with my laptop (and my cat, if he's in the mood), so I see the appeal.
The issue in your particular budget category is that there are no common desktop graphics cards between the RTX 3050 and 4060. The 4060 is of course faster than its laptop counterpart, but most systems that have one are £800 or more. The laptop 4060 is about 30% faster in gaming than the desktop 3050, although that varies significantly from one game to another. So there aren't many great options if you want to do better than the laptops I linked.
I did find this one though, for £700, with an RTX 4060 desktop (~20% faster than the mobile version) and an overall configuration that should run Sims 4 very well:
https://www.cyberpowersystem.co.uk/system/ultra-55-rtx-next-day-pc
You don't need any of the accessories, of course. A monitor will add to the sticker price, but if you're willing to do a bit of legwork, you can find a used monitor locally (Craigslist, Facebook Marketplace, Nextdoor) for not much money. The nice thing about a monitor is it's obvious when it doesn't work: you plug it in, you run some game to test it, and either you see dead pixels/bleeding/etc. or it looks fine. You don't need to pay first—most sellers will understand wanting to test before handing over any money. And then you can upgrade in a year or two, or never, depending on how you feel about your current monitor.
All this is to say that there's no one right answer, just what's right for you and your budget and your use case. And all these computers will handle ultra settings with room to spare, so you should get a good experience in any case.