Hi
I thought that was Eliza's name from the marriage, and Henry's birth reg, and so looked for Porter instead of Bunting.
One of the Pancras workhouse admissions.
18 Feb 1861
Eliza Porter 30
+ her two children Thomas 5, Charles, 2
Residence 5 West Str Bermondsey
Charles sent to Hanwell school 15 March
Thomas may have gone there too?
William Porter born in the workhouse 9 April 1861
All discharged 7 May.
On ancestry (may be on FamilySearch too)