The United Methodist Church was the result of the amalgamation of a number of groups which had split away from Wesleyan Methodism over a fifty year period. The reasons given for the secessions varied, but they were all variants on the theme of democracy within the church. Methodism could be described as having begun as a reform movement within the Church of England, and the Wesley brothers remained Anglican clergymen until the day they died, but many of those attracted to what we would now call a fresh expression of church during the evangelical revival were not attracted to the Established Church, and the leadership of the Established Church found many Methodists too “enthusiastic” and quite frankly insubordinate. From the start, then, Methodism contained a tension between conservative “Church Methodists” who wished to conform, and more radical evangelicals, who saw themselves as part of Dissent and read their scriptures in a different way.
Within five years of John Wesley’s death these tensions became too much for some members and the movement split.
Methodist historians have written at length on these matters in the Proceedings of the Wesley Historical Society and Methodist History, but if you are interested in reading contemporary accounts of all the controversaries of the first half of the nineteenth century then the following books may help you.
Gregory, Benjamin. Side Lights on the Conflicts of Methodism during the Second Quarter of the Nineteenth Century, 1827-1852, Taken chiefly from the Notes of the late Rev. Joseph Fowler of the Debates in the Wesleyan Conference: A Centenary Contribution to the Constitutional History of Methodism, with a Biographical Sketch. London: Cassell and Company, 1898, viii, 584 pp. see
Swallow, Thomas. Disruptions and Secessions in Methodism: Their Causes, Consequences and Lessons. London: Ralph Fenwick, 1880, viii, 215 pp. see
The full text of the infamous “Fly sheets” may be found here
They were reinforced by The Wesley Banner and Revival Record. London: Partridge and Oakey, 1849-1852. Vol. 1-2. and this may be viewed here
The whole story is covered in this book, recently reprinted
Beckerlegge, Oliver A. The United Methodist Free Churches: a study in freedom (1957) Wipf & Stock Publishers; Reprint edition (29 Aug. 2017) ISBN 978-1532638336
For a more recent study of West Yorkshire, where all the splits had an important effect it would be worth reading
Terry, James Gordan (1999) The causes and effects of the divisions within Methodism in Bradford, 1796-1857. Doctoral thesis, University of Huddersfield. which may be downloaded here