The restoration of the world to a primal condition (a sort of unity with the Divine) is also found in Jewish thought, where humanity can participate in the process of restoration by performing acts of kindness (tikkun olam). In the Hebrew Bible (Tanakh), the equivalent Hebrew word has the sense of the return of captives and the restoration of Jerusalem.
In Christianity, apocatastasis came to mean universal salvation, but discussion about it was complicated and incomplete. An anathema was pronounced against Origen's thought at an ecumenical council in 553, but traces of this thinking was found in other early fathers. The extent of salvation varied even in Origen's writings.
Other writers who embraced this view included Johannes Scotus Eriugena, who was an early medieval philosopher who also pointed out that God does not exist, because God is existence, and that communion is a symbolic act.
After the Reformation, the Arminians emerged as a distinct group among Protestants. Arminians rejected the Calvinist doctrine of predestination (the idea that only the elect, those chosen by God, would be saved) and embraced the idea that all who turned to God would be saved - so not actually universal salvation, but a universal offer of salvation. The early General Baptists were mainly Arminian in outlook (and indeed so are modern Evangelicals).
The Universalist denomination (which initially formed based around the belief that salvation applied to everyone unconditionally) existed in both Britain and America, but it was largely absorbed into Unitarianism. Several Unitarian churches started life as Universalist churches.
According to Wikipedia:
Christian Universalist ideas are first undisputedly documented in 17th-century England and 18th-century Europe and America. Gerrard Winstanley (1648), Richard Coppin (1652), Jane Leade (1697), and then George de Benneville in America, taught that God would grant all human beings salvation. Those in America teaching this became known as the Universalists.The Glasgow Universalist Church was founded in 1804 by Neil Douglas (Christodoulou, 1997) and had its roots in the Chartist movement. It was the first church in Britain to ordain a woman, Caroline Soule, in 1880. The General Baptists also largely embraced Unitarian views, and the General Baptist Assembly still exists as a distinct body within the General Assembly of Unitarian and Free Christian churches.
Gradually, the Universalist denomination in America came to embrace universalism in its wider sense, that is the idea that all religions have an underlying universal theme; this idea was also known as the perennial philosophy, which was the title of a book by Aldous Huxley, but the term has gained wider currency to mean the inner core of spiritual truth found in all religions.
An attempt to create a universal religion (atheist, secular and scientific) was made by Auguste Comte in the eighteenth century. This is described in a chapter in Alain de Botton's Religion for Atheists. Comte called his religion the Religion of Humanity, and it was influential in the development of modern humanism.
There was also a Druid form of universalism (which was more like the Perennial Philosophy). The earliest Druid revival groups were trying to get back to the primordial religion, which was believed to be a form of the ancient Hebrew religion brought to the British Isles by the Phoenicians. Pagan ideas were not really part of the Druid revival till the 20th century.
In 1961, the Universalist church in America merged with the American Unitarian Association to form the Unitarian Universalist Association (UUA). Prior to that, there was significant cross-fertilisation between Unitarianism and Universalism. One instance of such cross-fertilisation was the ministry of Kenneth L Patton. Patton started as a minister in the Disciples of Christ church, was then the minister of a Universalist congregation, and then of a Unitarian church. He was a religious humanist and his spirituality celebrated being alive, human, and the Earth and Nature. He was one of the editors of the 1964 UUA hymnbook, Hymns for the celebration of life, which includes several pieces of liturgy that he wrote.
Another modern proponent of universalism (in the sense of all religions sharing a core truth) was Forrest Church, who came up with the beautiful image of the cathedral of the world, which was an image to express the underlying sanctity of all religions, and their different perspectives on the holy.
One thing to be careful of when embracing universalism in the modern sense, is that a pick and mix approach to religion can be confusing and miss out the subtle nuances of different spiritual traditions. Each religion is like a language, rooted in its own culture, time and space. So perhaps a motto for universalists ought to be "Think global, act local". Acknowledge that the same light illuminates us all; that there is a universal truth; but there is not a universal religion, and that one's own beloved tradition has grown organically in its own particular culture, and that is good.