This is an English surname. It is locational from a place probably called Barstock, and if so translating as the 'boar pens' or similar from the Olde English pre 7th century 'bar-stoc'. Originally 'stoc' described 'a place', so this surname may refer to a farm or possibly even an area where wild boar were hunted or perhaps bred. Either way it does not seem to exist now and therefore this surname is one of an ever growing list estimated at about five thousand, of surnames which arise from 'lost' medieval sites. In addition locational surnames are 'from' names. That is to say names given to people after they left their original hones to move somewhere else. Spelling being at best erratic and local dialects very thick, often lead to the creation of 'sounds like' spellings. With lost village names there is often no way of telling the correct spelling. This name is recorded in the surviving registers of the city of London. An early example is that of Dorothy Barstock or Burstock, who married John Rawlings at St Mary le Bow, on April 26th 1709.