@Simswhynotplay £500 is right on the edge of where you might find an entry-level gaming desktop during Black Friday sales. It's not enough for a gaming rig during normal times, so if you're not interested in spending more, I'd suggest waiting until November. If you're willing to go a bit higher though, either of these would be able to run all current Sims 4 content on ultra graphics settings:
https://ao.com/product/ao22225-cyberpowerpc-ao22225-desktop-black-99497-253.aspx
https://www.argos.co.uk/product/4191874?clickPR=plp:5:60
https://www.currys.co.uk/products/medion-erazer-recon-e20-gaming-pc-intel-core-i5-gtx-1650-512-gb-ssd-10254876.html
The 16 GB RAM makes the third one a better option overall, but the first two could be upgraded later for cheap (another 8 GB RAM might cost £20) if necessary. And the first is only £520 if you're a member, so very close to your preferred budget. If you're ready to buy now, I'd consider this a win rather than waiting three months for a small price decrease.
The next-lower performance tier is within your budget, but these systems don't have a dedicated graphics card at all, only integrated graphics. This would limit you to medium-high to high graphics settings, at least with most expansions installed. This is the cheapest good example I'm seeing of that tier:
https://ao.com/product/ao22215-cyberpowerpc-ao22215-desktop-black-94327-253.aspx
This is the same, just more expensive:
https://www.argos.co.uk/product/4845388?clickPR=plp:1:60
If you're going to get a computer without a dedicated graphics card, I would absolutely invest in 16 GB RAM, likely as an upgrade you install yourself since the cheapest systems typically come with 8 GB installed. This is an extremely easy upgrade, even for a beginner, and as mentioned, memory is cheap, so don't let this put you off an otherwise good-enough option.
I've listed these computers in case you're interested in buying now but also so you get an idea of what's available. There are a lot of low-end systems in this price range too, so check the product pages carefully. In general, if you see a computer has a dedicated graphics card (the GTX 1650 in the first three examples), you don't need to worry about the other specs, which will be good enough—the GPU is the most expensive component and the critical feature for most gamers, so a manufacturer isn't going to pair it with other hardware that can't keep up. When looking at integrated graphics, it gets a bit more complicated, so it's best to ask if you're not sure.
In your position, I would really encourage you to consider a gaming system given that they're very close to your preferred budget and the upgrade is significant. But it's not required for Sims 4, especially if you're content with medium-high graphics settings.