Originally 'Moorish Dancers', or 'Moorishmen' indicating this old English practise may have been brought back with the Crusaders. Though this was most likely a reform of an existing British custom in which pagan dancers (following the Green Man) smeared their faces with ash from a ritual fire and went bonkers around town on Beltane.
The oldest formalised form was the Black Face Morris of medieval Kent, these maniacs painted their faces black with soot (associated with ash and fertility), dressed in rags and whacked each other with heavy sticks as part of a violent fertility dance to the sound of drum and pipe. They were accompanied by a fool/jester and a hobby horse. The event focused on the Green Man who was symbolically torn apart like Osiris (or the goat sacrifice of the Bacchanalia) at the end of the dance.
Another tradition associated with such dancers, as well as Mumming Plays and other customs, was 'Guising', once the practice of wearing animal skulls, and later masks of wood and cloth, allowing mythic representation. One common horse headed figure may be the origin of the more stylised hobby horse character.
This was associated with Moorish dancing, perhaps due to a reason as trivial as dark faces or possibily due to contact with Sufi ritual dances amongst the Moors. Hence the name.
Later in Kent they were referred to as 'the sweeps' and the dance was organised by the Craft Guild of chimney sweeps, after this dances dressed like sweeps, including the traditional black top hat with feather.
Their activities were attacked by the Church and supressed along with other Mayday customs. But survived in then more isolated rural districts. Later they were further suppressed by Oliver Cromwell.
Because of these suppressions, Morris Dance fragmented into isolated traditions which evolved seperately. Five dominant traditions remain today each with local variation: The Kent Sweeps; East Anglian Molly Dance, with ribboned peasant dress, hobnail boots and flat cap(!); Clog Morris, mass dancing in beads and clogs in Northern England; Border Morris, with its multicoloured ribbons and short sticks; and the famous Cotswolds Morris.
All of which are tame compared to the original, but Cotswold Morris is the most sedate of all. A heavily reformed Restoration style, it consists of set dances in white dress, covered with rossettes and bells, its dancers tapping each other with short sticks and flicking handkerchiefs. The dances are mixed and squeeky clean, the archetypal image of the modern morris. A far cry from its pagan roots.