This is apparently a very recurrent issue among Android phones, but the fix that applies to most doesn't apply to my phone. Most phones come with a Smart Wi-Fi, or in Xperia L's case, Location-based Wi-Fi, which you can disable and hopefully never have Wi-Fi respawn against command again.
In other phones you just have to disable notifications of present Wi-Fi networks, and the Wi-Fi can sleep tight until awoken.
However, I have disabled both modes, and my Wi-Fi still goes back on, no matter what. Can somebody shed some light?