That MAY be the sound of the damaged hairs dying. You MAY not hear that frequency again but that's unlikely.
Okay, so tinnitus, or ringing in the ears, can happen because of many reasons. There are three real kinds:
1) Spontaneous tinnitus can happen because of slight shifts in the acoustic systems of the ears, some of the hairs in the cochlea may amplify wrong and create a tiny feedback loop and ring for no reason. see this article about that kind of tinnitus here
However, that's not the kind of tinnitus you're referencing. That kind, post acoustic trauma, is more serious. This kind (which can result in hearing loss) results from either 2) one really loud noise OR 3) prolonged repetitive exposure to certain frequencies (like how your mom told you to turn your headphones down or you'd go deaf. Lower frequencies move a lot of air and can indeed be dangerous to your hearing.) Just how serious the damage from a single acoustic trauma event like the explosion from Children of Man would be to you would depend on just how loud the noise was you were exposed to, the frequencies of it, and how close you were.
So now that we've gone over the different kinds of ringing-in-the-ears (tinnitus), we can talk about how it works in this situation.
This is a great article on acoustic trauma tinnitus.
So these characters didn't rupture their eardrums or they'd be in a lot of pain and unable to hear at all in one side. Instead what happened was the tiny hairs that send electrical signals to the brain were probably bent and crushed (see awesome images on the article above of before, at, and ten days after acoustic trauma.) Three possibilities from here: either the hairs recover, they partially recover, or they don't recover at all. The most likely situation is that they do recover in a matter of days, leaving the characters with undamaged hearing. Some of the hairs (usually lower frequencies) may be more damaged that others. Those may dim or cut out frequency ranges in hearing. Multiple hairs cover the same range, so some of them may be out of commission while others survive, leaving you with diminished hearing of that frequency. However, that is not likely to be related to the buzzing/ringing frequency we first hear after acoustic trama, which is the sound of all damaged hairs freaking out and sending signals at once.
Great article on how we hear frequencies
source: Sound engineer. Protect your ears, guys!