As at 26 November 2022, this project is under new administration. 

According to Wikipedia, Burch is an English surname that most likely originated in Hyndley Birch, Rusholme, Manchester, England.  
The origins of the name can be traced back as far as 1500. The name can also be a variation of Birch, being derived from one who resides at or near a birch-tree.

But other authors believe this Surname descended from  de Burgh, a Norman surname which arrived in Britain in 1966.

You will find a great deal of history in 
BIRCH, BURCH FAMILY IN GREAT BRITAIN AND AMERICA
VOLUME I
WITH AN ADDENDA OF FAMILIES ALLIED TO BURCH FAMILY OF ENGLAND, VIRGINIA, MARYLAND, GEORGIA, ALABAMA, MISSISSIPPI, OREGON, AND OTHER STATES, if you click on the link below and download the Volume.  IF you download the .pdf version, the real information begins on page 26 (in the book itself, it is page 8).
https://ia803102.us.archive.org/1/items/birchburchfamily00smal/birchburchfamily00smal.pdf