The oldest club is the Bulldog Club Incorporated, which was formed on the evening of the 13th April 1875 in a private room at the Blue Post Public House, Newman Street, London.
The Bedlington Terrier Club was also founded in 1875, but was disbanded in 1882. The current National Bedlington Terrier Club are relative newcomers, from 7th June 1898
We are all pre-dated by the Kennel Club. It was founded on 4th April 1873 at a meeting at 2 Albert Mansions, Victoria Street, London. There is an interesting page about their history on their own website.