@hefffy8 You're not going to find a new laptop for £100 that would run Sims 4 with any success at all, and not even a refurbished laptop from a traditional store. At that price, your best bet is Craigslist or Facebook Marketplace, finding someone local who would be happy to receive £100 in cash, in person, for their used laptop. That makes finding the right model more complicated, since what's available is always changing.
In terms of specs, the simple details are RAM and storage: at least 8 GB and 256 GB, respectively, if you can. The processor is more complicated since there are so many models. But if possible, look for a laptop with one of these CPUs:
i5-1135G7
Ryzen 5 4500U or higher (second digit)
Ryzen 5 5500U or higher (second digit)
If that's not possible, an i3-1115G4 or a Ryzen 3 4000-series or higher would be less than ideal but still run Sims 4 okay. An Intel i5-12xxx could be equal to, or worse, than the ones above, depending on the ones above, and definitely better than the i3 and probably better than the Ryzen 3. A Ryzen 5 2500U or 3500U wouldn't be a bad choice if nothing else I mentioned is available.
Beyond that, there's a significant drop-off as you get to older or lower-end models, and I would avoid those entirely if at all possible. Feel free to list the specs of anything you're considering for me to take a look.