The four volumes of "The War at Sea were published between 1954 and 1961.

The "Editor's Preface and "Author's Preface" in Volume I, and "Author's Prefaces" in the later Volumes give accounts which may help you as to the origin of his sources.

One can appreciate that this production was done with the information in the public domain at that time.

Later research by others has helped to enhance it's contribution to history.

Unfortunately the Author himself cannot answer your question.

Good hunting

Phil