He was the seventh and youngest son of a WM coal trimmer from West Hartlepool, who later went into business as a butcher and provision merchant and seceded to the Wesleyan Reformers in 1850. He was born on 23 April 1852 and was educated at Anderson's School, West Hartlepool. At 16 he joined his older brother Thomas (1835-1905) in the family business. At his suggestion several steam ships were bought in 1877 from William Grey, a local shipbuilder. The partnership was divided in 1882, Christopher taking charge of the shipping fleet, which was merged in 1891 to form Furness, Withy and Co. He subsequently extended his business interests to include shipbuilding, marine engineering and coal, iron and steel engineering. Ultimately his various undertakings employed 50,000. Though politically a radical Liberal, a proposed profit-sharing scheme for his workers was rejected, but in 1895 he did establish the Furness Seamen's Pension Fund to provide for fifty Hartlepool seamen.
He was MP for Hartlepool 1891-1895 and 1900-1910, was knighted in 1895 and became 1st Baron Grantley in 1910, having joined the landed gentry by acquiring the 30,000-acre Manor of Grantley, near Ripon together with a number of church livings. It is suggested that later in life his UMFC and UM links were not strong, although he laid the foundation stone of Streatham UMFC church in 1910. He died on 10 November 1912.
One of his brothers, John Furness (1837-1902), who ran the family's provision business, served on the HartlepoolBoard of Guardians and was a trustee of Wesley WM chapel, Hartlepool from 1873. Another, Thomas Furness, was President of the West Hartlepool Temperance Society and Mayor of the town in 1891.