The case of the day is R. ex rel. Freedom & Justice Party v. Secretary of State for Foreign & Commonwealth Affairs, [2018] EWCACiv 1719. I can’t do any better than the court did in stating the facts:

The appellants are former members of the Egyptian government. Egypt has neither signed nor ratified the [UN Convention on Special Missions]. They contended that a person whom we will refer to as Lt. General Hegazy had been responsible for torture in the course of events which led to the downfall of the government of which they were members. In 2015 the FCO accepted the visit of Lt. General Hegazy and other members of his delegation as a special mission. The appellants requested that he be arrested. FCO and Crown Prosecution Service (“CPS”) guidance stated that special mission members were immune from arrest. No action was taken against Lt. General Hegazy. He left the United Kingdom at the mission’s end.

Can I start with an observation that may seem obvious to US lawyers but perhaps ridiculous to lawyers in the UK? It’s not at all clear to me why this case is in court, or whether there is any justiciable controversy. The dispute isn’t really about whether Gen. Hegazy should be arrested—that question was mooted by his departure from the country. The question is whether the government was wrong not to arrest him at the time. But do the victims of an alleged crime in the UK have the right to insist that the suspect be arrested? And in any case, how can the court remedy the injury, assuming they had such a right? In short, at least from an American perspective, it seems to me that this case would be more appropriately debated in a law school class on international law than in court.

In any event, the court held that the rule of immunity for special missions is indeed a rule of customary international law and that the common law recognizes and accepts it. I am not an expert, but the decision seems right to me, and justified by the same kinds of considerations that support a rule of immunity for permanent missions (though of course there will have to be a line drawn between missions on the one hand and ordinary official visits on the other). If the rule were otherwise the Act 1, Scene 2 of Henry V might have had a different ending!

KING HENRY.
Now are we well prepared to know the pleasure
Of our fair cousin Dauphin; for we hear 
Your greeting is from him, not from the king.
FIRST AMBASSADOR.
May't please your majesty to give us leave
Freely to render what we have in charge;
Or shall we sparingly show you far off
The Dauphin's meaning and our embassy?
KING HENRY.
We are no tyrant, but a Christian king;
Unto whose grace our passion is as subject
As are our wretches fetter'd in our prisons:
Therefore with frank and with uncurbed plainness
Tell us the Dauphin's mind.
FIRST AMBASSADOR.
This, then, in few.
Your highness, lately sending into France,
Did claim some certain dukedoms, in the right
Of your great predecessor, King Edward the Third.
In answer of which claim, the prince our master
Says that you savour too much of your youth,
And bids you be advised there's nought in France 
That can be with a nimble galliard won;
You cannot revel into dukedoms there.
He therefore sends you, meeter for your spirit,
This tun of treasure; and, in lieu of this,
Desires you let the dukedoms that you claim
Hear no more of you. This the Dauphin speaks.
KING HENRY.
What treasure, uncle?
EXETER.
Tennis balls, my liege.
KING HENRY.
We are glad the Dauphin is so pleasant with us.
His present and your pains we thank you for.
When we have march'd our rackets to these balls,
We will, in France, by God's grace, play a set
Shall strike his father's crown into the hazard.
Tell him he hath made a match with such a wrangler
That all the courts of France will be disturb'd 
With chases. And we understand him well,
How he comes o'er us with our wilder days,
Not measuring what use we made of them.
We never valued this poor seat of England;
And therefore, living hence, did give ourself
To barbarous license; as 'tis ever common
That men are merriest when they are from home.
But tell the Dauphin I will keep my state,
Be like a king and show my sail of greatness
When I do rouse me in my throne of France:
For that I have laid by my majesty
And plodded like a man for working-days,
But I will rise there with so full a glory
That I will dazzle all the eyes of France,
Yea, strike the Dauphin blind to look on us.
And tell the pleasant prince this mock of his
Hath turn'd his balls to gun-stones; and his soul
Shall stand sore charged for the wasteful vengeance
That shall fly with them: for many a thousand widows
Shall this his mock mock out of their dear husbands;
Mock mothers from their sons, mock castles down;
And some are yet ungotten and unborn
That shall have cause to curse the Dauphin's scorn.
But this lies all within the will of God,
To whom I do appeal; and in whose name
Tell you the Dauphin I am coming on,
To venge me as I may and to put forth
My rightful hand in a well-hallow'd cause.
So get you hence in peace; and tell the Dauphin 
His jest will savour but of shallow wit,
When thousands weep more than did laugh at it.
Convey them with safe conduct. Fare you well.

I am not going to review the judgment in detail. I do want, however, to mention its discussion of US state practice. Although the Restatement (Third) had been cited for the proposition that the United States does not yet recognize special mission immunity as a rule of customary international law, and although there has apparently been no definitive statement of the US position by the Executive, the court found that more recently decided cases showed that the best view of US law was that it does indeed recognize the immunity of special missions. Perhaps the matter will be made clearer when the Restatement (Fourth) is published.