Thomas “Fats” Waller’s London Suite was composed and recorded by the African-American pianist, entertainer and bandleader during his 1939 visit to Britain. This article is the first to examine the suite for its representation of a hybrid musical style. Its mix of stylistic markers of “hot” jazz with melancholic “sweet” music that references European classical music made the suite distinctive in Waller’s output and reflective of a different sort of hybrid musical aesthetic that came with his transatlantic musical tourism. Some original archival research is presented to help document the wartime circumstances that prevented the release of Waller’s recording until 1951. In the period between 1939 and 1951 Ted Heath’s all white British band released an orchestrated swing version of Waller’s piano suite. This is shown to be in many ways “hotter” in its swing than Waller’s original recording and the album was widely distributed in the United States. Analysis of contemporary reviews shows only when Waller’s recordings resurfaced was there a change in critical attitudes towards the hot jazz identity of Heath and Waller. Thus, the travel of Waller’s suite, back and forth across the Atlantic, shaped and reshaped not only its musical style but also perceptions of Waller and Heath with respect to apparently essential concepts of race and nation that were bound up with stylistic definitions of hot authenticity in jazz. Ultimately, Waller’s suite suggests the operation of a Jazz Atlantic, an outer-national critical conception founded on Paul Gilroy’s notion of the Black Atlantic, which might be extended to encompass a whole body of such hybrid-styled musical works and the critical discourse that surrounds them.