Laptops cheap for Sims 4

@Finfish12  You're not a pain; no one's making me answer.  (We all do this for fun, believe it or not.)

That laptop would have the same issues as your current one.  The processor is actually weaker than your current one—even though it has a higher base frequency, it's much less efficient.  Plus it's five years old.  The integrated graphics chip is weaker as well.  And the computers both have only 4 GB RAM, which isn't enough to run TS4 with all packs, plus Windows in the background.

I can explain what kinds of specs you should look for, other people here can do the same, but there simply isn't the kind of computer you want in this price range.  Even most laptops  around £600 wouldn't run TS4 with all expansions all that well, although (as you saw) there's occasionally a good option on sale.

Edit:  I saw your post in Other Sims Games and merged it here; it's best to keep the discussion about a single subject in one place.  (Plus, there isn't much discussion about specs at all there, since the issues with Sims 2 are generally not insufficient hardware.)  This model, the one with the AMD 530, is a step better than the others.  It still won't run TS4 on high settings, and I would expect it to struggle with the newer expansion packs even on the lower settings.  It does have a dedicated graphics card, but it's one of the weakest out there, at least among current models.  The processor is weaker than recommendations to run even one of the newest EPs, and it would likely not handle all of them together very well, if at all.