First of all: Frayn is a good writer. Best known as a playwright, this is not a play trying to be a novel-- there is dialogue, yes, but also lots of description and atmosphere. I applaud him for knowing which medium this story demanded, and for his versatility and skills.
The six immortal words that change Stephen's life are his best friend Keith's "My mother is a German spy."
Of course, any adult reader doubts that right away, but Keith is so odd and creepy that as he and Stephen (the narrator) set to trailing his mother there is an awful sense of tension and looming tragedy.
It's impossible not to think of L.P. Hartley's The Go-Between, if you've read it-- in that book likewise a man remembers being a child engaging in a mystery that was not what it seems. That book really does amount to heartbreak and inevitable tragedy. Partly that's because the adult reader understands what is going on better than the narrator.
In Frayn's novel, the older narrator has barely more insight than he did as a child-- and there's an irritating sense that things are being deliberately held back from the reader. The revelations, when we finally get to them, are not satisfying enough for me.
As a portrait of tension, suspicion and wartime paranoia, along with the awkwardness of adolescent friendships and loyalties, Frayn succeeds. But as a mystery, it's frustrating...the tension is both too much and not enough. The reader knows that whatever theory the boys come up with is wrong, and it takes too long to see that there is a mystery at all... so it never grabbed me with its urgency.
If you read it for the mood and not for the story, it is well written and worthwhile... for me it never really gelled.