PC for Sims 3 and 4, plus all expansions and mods

@DoggyMakeAwish  Are you looking to buy now or later?  If you're planning for a future purchase, there's not much point in making specific recommendations: prices change quickly, inventory turns over, and it's generally impossible to guarantee that the best options today will still be available in a few weeks, let alone a few months.

If you are looking to buy now, £700 is pretty much the starting price for a decent gaming desktop.  The most important detail is the graphics card: an Nvidia 1650 will run both Sims 3 and Sims 4 on ultra graphics settings, and the faster 1660 ti and the newer 3050 that falls between them are both more expensive.  That will likely still be true in a few months if you decide to wait, although the prices for systems with a 3050 may drop as the card becomes more widely available.

I had a look around and found a few good options.  One is a custom build from Overclockers UK:

https://www.overclockers.co.uk/ocuk-gaming-kinetic-h5m-micro-atx-intel-h510-configurable-comet-lake-home-pc-fs-1f7-og.html#t=d2

Upgrading the graphics card to a 1650 puts the cost at £710.  The processor isn't great but should be fine for both games, and the motherboard's socket would support a much stronger CPU, any 10th- or 11-th gen Intel Core model, if you ever need one.  The system comes with 16 GB RAM, very nice to have if not strictly necessary, and a 500 GB solid state drive, which is more than enough storage for both games.

An SSD is very helpful for Sims 3 in particular because it dramatically speeds up loading times, not just for the initial loading screens but also during travel transitions and when you open CAS or Edit Town.  (Windows will also run significantly faster on an SSD, as will many other apps, although it doesn't make as much of a difference to Sims 4.)  You could save a  bit of money by going with the 1050 ti rather than the 1650, but for that small price, I think the faster card is absolutely worth it.  Overclockers PCs generally have good build quality, not premium-level but unlikely to present any problems.

These two options on Amazon would also work:

https://www.amazon.co.uk/HP-Pavilion-Gaming-Desktop-TG01-1042na/dp/B08SQRZ9PZ

https://www.amazon.co.uk/CyberpowerPC-Wyvern-590-Gaming-PC/dp/B074JCL7TQ

The 1650 Super in the HP is slightly faster than the others, but the HP also only has 8 GB RAM and a mechanical hard drive rather than an SSD.  The 256 GB SSD in the Cyberpower option is large enough for Windows and both games, but you'd need to be careful about free storage and move any overflow data to the HDD, or else install Sims 4 on the HDD.  The HP's processor is the best of the three, and the Cyberpower's the worst, but all of them should be fine.  These two AMD processors also use the same socket, meaning they'd take an upgrade to a 5000-series AMD CPU if you ever wanted one.

In terms of build quality, I'd expect the Overclockers PC to be the best of the three, followed by the Cyberpower model.  HP gaming PCs aren't bad but also use lower-end parts made specifically for the company; the other two use the same components you'd buy if you were building your own PC.

If you have more questions, feel free to ask.

Thank you very much for your fast and in-depth answer! Also for the explanation about the reasoning behind choosing certain parts.

What would you consider a good budget for a gaming pc? That way I can always save for a while longer, and get something that will last and save myself the hassle from getting something cheaper but having to replace it sooner rather than later.

Again, thank you very much!

@DoggyMakeAwish  A "good" budget for a gaming PC depends entirely on what you want to do with the computer.  In your position, I'd prefer to get a 1660 ti or Super, but it's not critical.  Like I said, the 1650 will still run both games on ultra settings; it's more a question of having some breathing room for more demanding custom content or future Sims 4 packs, or perhaps a different game I don't yet know I'd want to play.

You can see on the Overclockers site that upgrading to a 1660 Super would cost another £120 above the price for a 1650, which is an entirely reasonable price.  (Systems with a 1660 would typically be £900 and up.)  I'd certainly recommend it for someone whose budget could fit the upgrade.  But aside from the obvious benefit of getting your computer sooner, the other reason not to wait is that you never know what might be available down the road, and at what price.

The quality of the build is actually not entirely dependent on the price.  You could get a £1600 system with a better processor and graphics card but with a low-end motherboard and power supply.  Those are the systems that most often need to be replaced in a few years, especially since some manufacturers (Dell is a big offender) use nonstandard parts that are difficult to replace and impossible to upgrade.  In contrast, a system with a weaker CPU and GPU may be built to last and to take upgrades without any trouble.

As an example, the system from Overclockers UK comes with a standard motherboard, not a great one but one that should work for as long as you have the computer.  The power supply is similar, and in addition it's strong enough to support a somewhat faster graphics card if you decide you need one in a couple years.  The same goes for the processor, although you'd be limited to models that use the same socket.  (That's the 10th- and 11th-gen Intel CPUs I mentioned before.)  So that might be a £250 upgrade for a new graphics card rather than another £700 for a new computer, assuming the graphics card market comes back down to earth sometime in the next two years.

If you'd rather wait and save up a bit, feel free to come back when you're ready to buy.  I'll be around.