Showing The Yellow Room Conspiracy by Peter Dickinson

Two ex-lovers, he merely getting old, she already slowly dying, hear a radio quiz programme about a scandal in which they were both involved at the time of the Suez Crisis. Some time later she asks him to tell her how he killed one of the other participants. He replies that he'd always imagined she had done it. Who then did?
Little by little they re-tread the maze of high politics, espionage and shady property deals and find the answer.