There are several origin theories:[1] all may be true as there are distinct groupings of Paddicks across England.
The first group, from the Somerset, Dorset and Bristol area, is thought to derive from the Old English paddock meaning an enclosed or fenced area of land.
The second group comes from the English Midlands, particularly Shropshire and Staffordshire, though also through time from Birmingham and Lancashire.
The vast majority of people with the last name Paddick or Paddock in England are descended from this group.
[1] The third group is concentrated around the South East England coast, particularly in the counties of Hampshire and Sussex, and this group is a variant of the surname Padwick.