Wedgwood was the youngest son of Francis Wedgwood and his wife, Frances Mosley. Wedgwood helped incorporate Josiah Wedgwood & Sons Ltd. in 1895. Elder brothers Godfrey and Clement were also in the business. He was the great-grandson of the potter Josiah Wedgwood. He married Emma Elizabeth Houseman in 18 April 1871 and they had six children:
- Kennard Laurence Wedgwood (1873-1949), partner in Wedgwood & sons.
- Mary Frances "Molly" Wedgwood (1874-1969)
- Gilbert Henry Wedgwood (1876-1963)
- Clement John Wedgwood (1877-1954)
- Geoffrey Walter Wedgwood (1879-1897)
- Unnamed daughter (born and died 22 October 1882)
- Obituaries: Mr. Lawrence Wedgwood (sic). The Times, Wednesday, May 07, 1913; pg. 11; Issue 40205; col C .
- "Lives of the Wedgwoods: The fourth generation". The Wedgwood Museum. Retrieved 2010-02-28.
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