Can you imagine that in the UK?
"The idea is to create a button that parents can download and install on their children's computers: if they then encounter serious trouble online, one click on the button would instantly connect them to police or child protection groups."
Imagine the scene in the UK, the kid visits a site, presses the panic button on their computer. The rozzers rush round to seize the computer, arrest the kid & parents, get a lot of DNA samples, perhaps prosecute the kid for possession of extreme porn.... Is there something encrytped on the computers they can demand decrypted....maybe a prosecution or two in it RESULT!
On balance, I think the kid is better contacting the parent. The rozzers main interest is in arrests, because that how their performance is measured, the child protection groups always exaggerate problems to maximize fund raising (shall we stop it now?)... so not a good thing to let your kids bypass you.
If you recall the teacher who was arrested in the US when some virus on the computer popped up a porn site, as if *she* was to blame? That's you that is!