It's been a long while since there's been a truly great budget gaming CPU that's actually been available to buy. AMD's Ryzen 3 3300X filled that hole admirably when it first launched back in May last year, but the sheer popularity of that £115 / $120 CPU has meant that it's been out of stock almost ever since. Indeed, AMD still haven't released a Ryzen 5000 successor for it, and even Intel's 11th Gen Rocket Lake earlier in the year didn't yield any promising Core i3 candidates, either, with the chip maker stopping firm at the Core i5-11400 and i5-11400F, the latter of which is on test today.
The Core i5-11400F is fundamentally identical to the 11400 - it's just that the F model doesn't have any integrated graphics built-in. As such, you'll need to pair it with a graphics card if you want anything to appear on your monitor when you come to turn it on. Otherwise, they're exactly the same chip. And for lack of any other competition right now, this £150 / $230 CPU is probably the closest thing you'll get to a great budget gaming CPU in 2021.