Found [web] (author list, 10 records, and Google snippets)
Soddy, The Story of Atomic Energy (London: Nova Atlantis, 1949).
MS Museum 121: Nobel Lecture print (Stockholm 1923); "The Kiss Precise | The Hexlet | and The Bowl of Integers" (Nature 137, 1021, 1936; 138, 958, 1936; 139, 77-79, 1937, with replies); "The Cubic Equation with Three Real Roots: Its Geometrical Diagram and a machine that solves it" (2nd ed., London: New World Publications, 1956); 1927 printed petition to the Privy Council on the Aldrichian Praelector post.
MS Stapleton 258: "An Independent Scientist's Views on the Economic & Political Possibilities of Atomic Energy for the Future" (London, 1947, lecture pamphlet); "Can a Nation be Saved by Budgets and Ever-Increasing Taxation?" (The Torch of Truth, May 1948).
The Chemistry of the Radio-Elements (1911; Part II 1914); Matter and Energy (Williams and Norgate, c.1910, Home University Library), presented by Oriel College.
Snippets: "Atomic Transmutation ... from Memoirs of Professor Frederick Soddy" (London: New World Publications, 1953) [Muriel Howorth's book]; "In Commemoration of Professor Frederick Soddy ... formerly President of the New Europe Group" (1957); F. A. Paneth, "A Tribute to Frederick Soddy", Nature 180, 1085-1087 (1957); Soddy's address to the 5th Lindau meeting (dated "12.VII.", year cut off in the snippet; 1955 if the meetings are counted from 1951, [memory] medium); an "Eccentricity" exhibition page featuring Soddy.
How it bears on the claims
Claim 6-7: the 1947 pamphlet and The Story of Atomic Energy (1949) are Soddy's own post-bomb statements on the economic and political consequences of atomic energy, the theme the 1909-1920 books announce. Not in the folder; worth obtaining.
The 1953 Howorth "Atomic Transmutation ... from Memoirs of Professor Frederick Soddy" is a memoir-based source written with Soddy's cooperation (Howorth was his literary trustee: an interested party in his reputation).
The HSM also holds the engine model and the cubic machine (see Archives Hub note); these are Soddy's own inventions outside radioactivity.