I had a quick look at the 1881 census, Charles Henry Cawkwell born 1866 in Hull, son of George Cawkwell labourer aged 46 born Tunstall Yorks and Mary aged 43 born Hull. Resident at 1 Church Street, Charles a cotton factory hand.
Hi Margaret, welcome. I have Cawkwells too! The Cawkwell (also Coquewell and Coquell) name originates around the Isle of Axeholme near to Thorne and Crowle, so as you get further back I'm sure you get to that area. Look on the Lincolnshire and West Yorkshire sites as well as Hull and East Yorkshire. Lots of people moved to Hull from Thorne including my ancestors who were boatmen. There's a useful site with Thorne parish records transcribed on it, just google it.