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Officially named Unitas Fratrum (Unity of the Brethren), it originated in Bohemia when Jan Hus, a priest and philosopher, objected to some of the practices of the Roman Catholic church, and wanted to return to the Eastern Orthodox church of Bohemia and Moravia. The movement gained much support, but was eventually subjugated by the Catholic church. In 1722 a group of Bohemian Brethren from an illegal remnant of the movement, sought sanctuary at Bethelsdorf, the estate of Nikolaus Ludwig von Zinzendorf.

The movement grew via missionary work and initially the missionaries only passed through London on their way to the slave communities in America and the West Indies. But waiting for their ships they needed to meet and pray, and perhaps could not restrain themselves from evangelising wherever they were. In London they initially met in private homes and then in 1740 began using a chapel in Fetter Lane. The Moravian Church now has over 800,000 members worldwide.

London Details has a good post about the Moravians' plot of land in Chelsea.

The Moravians do seem to have been unusually successful at founding and sustaining settlements. Between 1744 and the 1780s they founded 7 villages across England and Ireland, but none near London.