Well, I would suppose it would depend on just how well outfitted the school actually is.
My first secondary school was very deprived, even by the standards of that time, and there was very little in the way of history books, computers, or anything else that would be immediately useful. On the other hand, there were a few teachers who really knew their stuff and could certainly lay the groundwork for tech uplift if they were given time. The school was a boarding school in Fife so there would be no need to immediately evacuate or intern the pupils. In the long-term, of course, they’d need to be farmed out to foster parents.
My second school was a lot more advanced; there were hundreds of computers, dozens of books - mostly very basic when it came to history and technology, but still useful - and a lot of other things. I daresay the government would take everything into custody, and try and look after the children while assessing the history windfall and picking out how best to use it. I don’t think 1940 Britain could have avoided the collapse of the British Empire, but they could have traded advanced technology to get better terms for America and cushion the fall as much as possible. Some of the kids were of Asian descent and would probably know at least something that could be used. Some of the teachers were old enough to remember the 1960s if not earlier. (We did say that one really old teacher dated all the way back to the Stone Age, but this was probably untrue <grin>)
In the short-term, I don’t think much will change. Churchill will know that Operation Sealion is a non-starter. He may also realise that aiding Greece at the expense of losing a chance to beat the Italians in North Africa would be a mistake. He may push to keep French North Africa out of the war, if possible, and then send reinforcements to India when he realises that Singapore is doomed. He may or he may not warn the Americans about Pearl Harbour - on one hand, the Americans would see it as a betrayal (unless you buy into the theory FDR allowed the act to ahead); on the other, Japan is doomed by the mere act of starting the war and Churchill knows it will work out for the best. Either way, Britain will make a better showing in the early days of the Far East war. From there, events will spin unpredictably. For example, if the North African War ends in 1940/1, will the Allies attack France in 1943 rather than 1944? What will this do to the Russian War?
In the long-term, after the war, I think a great many things will change. A person from the 1940s will regard 2023 with a degree of horror. They will be adamantly opposed to immigration, even from Commonwealth states, and they’ll think a lot of what we take for granted is utter madness. Even something as simple as women working outside the home permanently, instead of just a war measure, will horrify them.
Worse, if the kids are stereotypical enough, the 1940s people will see it as a result of a lack of discipline; perhaps conscription will be kept longer in this timeline, or be replaced by a public works scheme. On the plus side, technology will advance faster - based on information recovered from the school - and there’s at least a chance the USSR will collapse earlier and/or the space race and nuclear power will develop faster than in the original timeline.
It’s possible you could get a set of interesting stories out of this. There was a girl in my school, back in 2000, who was very much determined to rise to the top. She was clever, ambitious, and not afraid to speak her mind. In our time, she could have risen; in 1940, the opportunities would be great deal fewer. Female professionals were very rare and her attitude would rub the 1940s people the wrong way. Or you could have the typical tech-tinkering nerd suddenly finding himself very much in demand because he knows more about future tech’s than almost anyone else. Or a football star having to cope with army training. Or … Who knows?
This could make a cool anthology.
