Yes, this is straightforward (if somewhat tedious). Avowals and Denials begins with a note:
The essays of which this book is composed are reprinted, often with slight alterations, from the Illustrated London News, by kind permission of the proprietors of that paper.
The original dates can thus be found using the British Newspaper Archive. This would ...
For completeness, I leave here the straightforward and tedious search.
Monsters and logic 6 january 1934
On Christmas that is coming 23 December 1933
On the man on the spot 26 August 1933
On Shaw and his back girl 31 December 1932
On the atheist museum 19 November 1932
On the new prudery 11 March 1933
On the return of the barbarian 5 August 1933