William and Harriet had 3 girls and the Batchelor name would have died out with them but the information I have is noted below. 

Henrietta Batchelor (1859- ) 

Henrietta born in 1859 and was a cook and living with her mother in the 1881 census.  

In the 1891 Census she was in service as a cook for Ferdinand Lowenthrall a German Commission Agent and his family who were living at 205 Adelaide Road, Hampstead. 

No trace in 1901 and presumably she had married or died. 

Harriet Batchelor (1860- ) 

Harriet born in 1860 and was a laundry maid and living with her mother in the 1881 census. 

In the quarter to June 1886 she married Samuel Benjamin Lancaster in St Georges Hanover Square. They had three children all born in Hammersmith; James born 1885 Jane born 1888 Jane and Elizabeth born in 1890. 

In the 1891 Census now Harriet Lancaster she was living with Samuel ( 32) at 33 Leffum (?) Road Hammersmith . Samuel was a horsekeeper. James was 6, Jane was 3 and Elizabeth 7 months. 

In 1892 Phyllis was born in Hammersmith. 

In the 1901 Census Harriet aged 40 was living with Samuel (42) at 6 Holcombe Hammersmith. Samuel was a groom horsekeeper.  James who would have been 16 was not there but Jane (13), Elizabeth (10) and Phyllis (9) were living with their parents. 

We have no idea what happened to the Lancaster family in the 20^th century. 

Mary Jane born in 1870 

Cannot trace what happened to Mary J. She probably got married before the 1891 census when she would have been 21.