Owen Dudley Edwards writes (British Children's Fiction in the Second World War, p.212) of Saville's Mystery at Witchend as "the BBC 'Children's Hour' serial subsequently given book form". In fact, Mystery at Witchend was published on 1st October 1943, and broadcast on Friday afternoons, 5.20 - 6.00pm for four weeks starting Friday 8th October. The adaptation of the book was by Barbara Sleigh, an author in her own right who worked with her husband for the BBC. Sleigh's script is now published(2008) by David Schutte (ISBN 978 0 9546801 5 1) .
ODE talks elsewhere of simultaneous publication and broadcast, which is about right, since the decision to broadcast and the preparations must have been pre-publication. Whether the story had been commissioned for broadcast is beyond the evidence - a new untested writer being asked to write a war story is unlikely, and more likely that Sleigh knew Saville (Geoffrey Trease was a common friend and confirms the friendships in his autobiography) and liked the story which she had read pre-publication (although I am uncertain whether she knew Saville prior to the broadcast decision). A spy story perhaps suited the feel of the time, when threat of invasion had receded and children could feel empowered to contribute to the war effort. In fact, MI6 histories report that by this time spies were not much of a threat so that popular vigilance endangered innocent aliens more than spies.
ODE gives a detailed footnote (352-3 fn45) confirming these timings and commenting on the experienced cast. This had not been an economy production. ODE comments at length (253-7) that Mystery at Witchend was Saville's best book.