The abolition of school corporal punishment (SCP) followed a ruling of the European Court of Human Rights (ECHR) – which sits in Strasbourg, France. You are correct that the International Court of Justice sits in The Hague (Den Haag or ‘s-Gravenhage), Nederland but that’s a different court. Both are separate from the EU.
That ECHR ruling did not prohibit SCP. It merely found that the UK had failed to respect the parent’s philosophical convictions (Article 2 of the convention). It is likely the more severe levels of SCP would be prohibited under Article 3 of the convention which bars “inhuman or degrading treatment or punishment” but the court did not rule on that.
One suggestion at the time was that the UK could comply with the ruling by simply allowing parents to opt their children out of SCP. This was rejected as being unworkable despite many schools already having a policy of exempting roughly half their pupils for SCP. The proposal, if accepted, would have simply changed the selection criterion.