This two-part article re-opens the debate between Political Marxism (PM) and Leon Trotsky's theory of uneven and combined development (UCD) on the question of the origins of capitalism in late medieval and early modern England. At the center of this controversy stand divergent assessments of the relative importance of 'endogenous' and 'exogenous' causes of the rise of capitalism in England and non-rise in much of Western Europe. Part l asks: can UCD provide an anti-Eurocentric International Historical Sociology, which explains the extra-European sources of the origin of capitalism in Europe and the rule of the West? It introduces into the recent literature in International Relations on UCD as a new theoretical framework for International Historical Sociology, and provides a detailed critique - theoretical and historical - of Alexander Anievas and Kerem Nisancioglu's research monograph "How the West Came to Rule:The Geopolitical Origins of Capitalism'. Against the book's main theoretical thesis, which claims that major traditions in Marxist Historical Sociology, including World Systems Theory and Political Marxism, succumb to Eurocentric accounts of the rise and expansion of capitalism that elide the contribution of the non-European world, the article suggests that both paradigms incorporate international relations into their conceptions of historical development, while judiciously demonstrating why extra-European influences were not decisive for capitalism's origins, as distinct from its further development in Western Europe/England. While part I covers the theoretical and methodological aspects of the differences between PM and UCD, part II, published in a subsequent volume of SLR, will show how the historical deployment of UCD in Anievas and Nisancioglu systematically fails to consider how the extra-European world caused, rather than merely contributed to, the rise of capitalism in late medieval England. This part includes a refutation of the arguments that the late medieval 'Black Death' pandemic, the rise of 16th Century large-scale long-distance trade, intensified Ottoman-Habsburg military rivalry, Atlantic Colonialism and slavery, and 'bourgeois revolutions' were decisive, either singularly or collectively, for the origins of capitalism in England. Ultimately. the two-part article concludes that the book lapses into a reverse Eurocentrism and a new world-historical teleology in which the history of the non-West is reduced to a prelude to how the 'West' came to rule.