Looking again at the Mower family who were taken into the workhouse in 1858, because the husband, John Mower, was ill.
The children were: Emma 18; Mary 16; Jane 15; John 5 and twins William & Henry age 13 months.
If William and Henry were only babies when their father died, it's possible they didn't know his name or occupation. (I've been surprised by the amount of children (legitimate) I've come across who didn't know their deceased father's correct name.)
The two boys were in Hanwell workhouse in 1871.
There's a William Mower getting married in 1878 who is a police constable. Maybe that's where Henry got the idea from.