As far as I know the name Muxlow (or Mucklow or a myriad of different spellings) originates from the village of Mutlow, Worcestershire. The Mucklow family were living at Arely certainly in the 14th century (see Worcestershire visitations). A branch of this family settled in Desford, Leicestershire in the late 16th century. At this point the name is often written as Muxlow - perhaps due to the proximity of Kirby Muxlow.From there a branch moved via Upper Broughton, Notts, East Markham, Notts to Leadenham, Lincolnshire, establishing the Lincolnshire Muxlows. Nonethless the name continued to be written both as Mucklow and Muxlow throughout the 18th century.