Because your 1861 link didn't work for me I had to look elsewhere to find out who you were looking for and that came from an old thread saying this:
I didn't really study the opening post in that thread at the time, because I was only interested in finding on which census you were looking for George White transcribed as 31 with a wife Mary.
Now I've read it again, still probably not properly, it sounds as if you are thinking 2 Cottage Place in Shoreditch is the same address as 2 Cottage Place in Poplar (Bromley St Leonard), but surely it can't be? I also haven't yet understood why you were interested in George White in any case? I wasn't sure if it was him you were following or just the person at the place where Thomas Sayer was born later in the year?
If it's the address, then Thomas was probably born where these people were living:
1861 census, 2, Cottage Place Hoxton, St Leonards Shoreditch, London & Middlesex
Jeremiah Banes head married 40 porter b Colchester, Essex
Esther Banes wife married 44 b Shoreditch, Middlesex
Thomas Banes son 14 Errand b Aldgate, Middlesex
Esther Banes dau unm 19 shirt maker b St George in the East, Middlesex
Maybe I've missed the point, but the opening post on the old thread was too difficult for before all my morning mugs of tea.