The verdict? There is no possible way that the ICC or ICJ would hear such a case.
According to Bir Zeit University international law professor Yasser Al-Amouri, there is no possibility of litigation before the International Court of Justice and the International Criminal Court, since the Balfour Declaration is not within the jurisdiction of either court. The International Court of Justice considers legal matters on the basis of the consent of the parties to the dispute to resolve the case, which is highly unlikely that Great Britain will consent to being sued there. The International Criminal Court, is unlikely to say that it has jurisdiction over a case like the Balfour Declaration, for more than one reason, including the fact that it was written in 1917 and that it seems highly unlikely that Balfour is a war crime or genocidal.
However, Amouri says, the PLO can use diplomatic means to pressure Britain to issue an apology, which would be considered a great victory.
An Al Monitor article last summer described a possible (albeit also unlikely) path for diplomatic pressure on Britain:
Expert in international law Hanna Issa told Al-Monitor...“I expect the PA to follow these successive steps; it should first resort to the [UN] Security Council to adopt a resolution condemning the Balfour Declaration — which will [most probably] be vetoed by Britain since it is a permanent member of the Security Council. [In this case], the PA should then address the UN General Assembly and demand it to consider the case in accordance with the Uniting for Peace resolution [No. 377] issued in 1950, which gives the UN [General Assembly] the right to intervene if the Security Council fails to exercise [its responsibility] should one member [Britain, in this case] use its veto. The resolution gives the UN the right to review the case and make recommendations to take collective measures aimed at maintaining peace and security, and these measures include the formation of a special court to look into the case.”
That is sort of insane. The Uniting for Peace resolution to override the Security Council has been rarely invoked, and it sure won't be for something as stupid as this.
In the end, this is another stunt by Mahmoud Abbas, who has a history of preferring stunts than actual leadership and working for peace. One can only hope that Great Britain and the rest of the West will not only not be influenced by such threats, but would learn from them how unserious the Palestinians are about actual peace.