This is a long shot!
In 1871 there is a William Banfield b. Devon aged 64, living in Gillingham with wife Louisa aged 40 b. Devon and children including a Jannie Banfield aged 3, born Chatham.
RG10/911/56 p 22
Given the age difference between William and Louisa and the fact that there is a big gap in the ages of the children (20, 18, 14, 5, 3, Jannie being the youngest), I am wondering if Jannie is Janneta - Louisa's daughter and was born with another surname?
William is however a stone mason, not a policeman.
Bev