The modern ecumenical movement is typically traced back to the World Missionary Conference in Edinburgh 1910. I haven't seen anything in print about the history of ecumenism before that date. There certainly must have been attempts to bring the traditions together although doctrinal controversies and nationalism must have made this difficult to support.
It is remarkable that Wesley drew on five traditions in developing his innovative take on the Christian faith. Runyon examines each of the traditions he has identified on the pages following page 207 of The New Creation. The five traditions he lists are Puritanism, Anglicanism, Moravian Lutheran Pietism, Roman Catholicism and Eastern Orthodoxy. He writes on page 213:
It is not surprising, therefore, that the claim has been advanced that Wesley combines the Protestant emphasis upon justification with the Catholic emphasis upon sanctification. There is a certain cogency to this claim, but it seems more accurate to say that after 1738 he placed the Lutheran doctrine of justification within the context of a doctrine of sanctification derived ultimately from Eastern patristic sources. Although parallels to western Catholic sources are clear, important distinctive features are traceable to the Eastern Fathers, and this background needs to be recovered to place Wesley properly in context.
Modern Methodism has always professed a strong affinity to ecumenism and possibly its origins in the leadership of John Wesley has something to do with it. Certainly his emphasis upon his Three Grand Scriptural Doctrines suggests a way forward that in effect overlooks the major differences and focuses upon what Wesley saw as the common features of all Christian traditions. This is a thought developed in his sermon 'The Catholic Spirit'. It is difficult to say whether this approach has any mileage today.