[1] He received his Doctor of Philosophy from the London School of Economics in 2002 with a thesis titled The British Battalion of the International Brigades in the Spanish Civil War, 1936–1939.

[4] George Esenwein, writing in European History Quarterly, questioned "Baxell's pointed efforts to shift attention away from the complex web of political and ideological circumstances that inevitably shaped the experiences of the British battalion", including their connections to the Soviet Union and Stalinism, and argued that he failed to "offer a compelling case in support of his view that the British battalion was composed mostly of independent-minded volunteers who maintained a considerable degree of autonomy from the communist command structures of the International Brigades."

Esenwein concluded by noting, "Even if Baxell's own advocacy of the brigadiers' cause tends to colour his historical judgements, we have him to thank for correcting misconceptions that have unfairly tarnished the reputation of this distinguished group of committed citizens".

[4] Baxell is also the co-author, with Angela Jackson and Jim Jump, of Antifascistas: British & Irish Volunteers in the Spanish Civil War (2010), a book of short texts and pictures.

[7] Baxell described the book as "the first to place the Spanish Civil War within the context of the volunteers' lives, rather than the other way round"; and said it seeks to deliver its narrative "from the perspective of the participants themselves using, wherever possible, their own words".