Bigwood was born at Bristol. He was educated at Cotham, Bristol and at St John's College, Cambridge (BA. 1853, MA. 1866). He became a partner in the firm of Champion & Co. mustard and vinegar manufacturers located in Finsbury. He was a member of the Society of Chemical Industry and a strong proponent of food product purity.
In the 1885 general election, Bigwood was elected Member of Parliament for Finsbury East with a lead of 20 votes but lost the seat against the trend in the 1886 general election by 61 votes. He was elected MP for Brentford in a by election in 1886 and held it until the 1906 general election. On 17 January 1906 he was appointed a deputy lieutenant of Middlesex.
Bigwood lived at Twickenham and died at the age of 80.
Bigwood married Marian Webb of Torquay in 1862.
|Parliament of the United Kingdom|
|New constituency|| Member of Parliament for Finsbury East
| Member of Parliament for Brentford