In 1934, a child's construction toy - Meccano - was used to build the first differential analyser in the UK. Initially intended as a proof-of-concept model, the original Meccano differential analyser proved so successful at resolving equations that many subsequent Meccano and non-Meccano analogue computers were built in the UK. These machines were used before, during, and after the Second World War as research instruments and teaching devices. Despite this, the part of the original Meccano differential analyser that has sat in the Science Museum since 1949 has been used to tell a Whiggish history of computers that focuses on digital machines at the expense of analogue mechanisms. While historians of computing today define their work in opposition to this linear-progressive account of computing, this approach featured prominently in academic literature until the turn of the millennium. This thesis explores Hartree and Porter's original Meccano differential analyser as an analogue computer, using it as a case study to explore the complex relationships between Meccano, play, science, and engineering. In doing so, it considers the object as an assemblage of its Meccano materiality, its instrumentality as an analogue computer, and its career as a collected object in the Science Museum. It deconstructs these different elements of the assemblage and explores how they are part of wider, external assemblages that have their own public histories. The thesis considers the changing materiality of Meccano as an object from 1901 to the present day, analysing marketing materials, the Meccano Magazine, and the voices of the Meccanomen to challenge the conventional, synchronic history of the toy as an unchanged engineering tool. It uses the Meccanomen's popular publications together with archival sources and interviews to historicise the 'alternative' version of the Meccanomen's movement, making it possible to see how individuals attached a variety of personalised meanings to their Meccano hobby. It also explores the object's instrumentality as an analogue computer, beginning with a detailed 'nuts and bolts' comparison of how the original Meccano differential analyser worked with how it was presented in academic and popular publications in 1934. It then brings together the stories and applications of other differential analysers constructed in Britain during this period, to provide further case studies about the role of these computers during the Second World War, and how they have been displayed in museums. The thesis then draws on these analyses by telling the story of the 'Trainbox' object that was collected by the Science Museum in 1949. The 'Trainbox' was comprised of parts of the original Meccano differential analyser that Hartree used to teach the principles of differential equations and integration after the Second World War. Through exploring how the public history and voices of the object have been changed in different exhibits in the museum, this thesis demonstrates the complex relationship between different parts of object's assemblage in a variety of contexts over time. The final part of the thesis builds on these deconstructed elements by reconstructing the original object as the Kent machine, a historical reproduction designed to recover elements of the tacit knowledge used to build it in 1934. It finishes by exploring how these new understandings of Meccano and analogue computers were used to co-curate a new public history for this curious object, using the 'shared authority' of myself, the Meccanomen, and audiences we engaged with the Kent machine.