It's a big undertaking and usually only works if there is some more specific info known about an individual.
I discovered, immediately upon first researching him, that there was nothing in any record about my gr-grfather before his 1883 marriage; he had sprung from nowhere, with two distinctive given names and very unusual surname. I did not know where he was born, but I knew his (approx) year of birth.
Unfortunately for me, we knew that after he married in England 1883, he was in Australia for the 1891 census, and I could not find him in 1901 for love nor money, to at least find what age and place of birth he gave. He then immigrated here to Canada.
Let's say their names were, for illustration:
My gr-grfather was Edward Arthur Moonwalk.
His daughter was Alice London Moonwalk.
His father was Fiscus Moonwalk.
I got an early clue: when searching for the birth of a daughter of his that we had just learned died in infancy, Alice Moonwalk, I found that she was Alice London Moonwalk -- and I found the marriage of a person a generation older with the identical given names and surname, otherwise unique. No idea how they were related, but they had to be. And when I searched for someone with the same given names as my gr-grfather born around the same time, I found an Edward Arthur Smith, let's say (the surname was nearly as common!).
Eventually, I found the family that matched all these clues, in the 1861 census: that Edward Arthur Smith, with a sister named Alice and a father named Fiscus. Born in Cornwall. And when I finally found my gr-grfather in London in 1901 (his surname bizarrely mistranscribed at two different sites), he gave the same place in Cornwall, for his place of birth. So both he and his sister (that we had never heard of) had adopted the same fake surname, and both had assigned it to their father when they married, while retaining the father's real given name: Edward Arthur Smith and his sister Alice London Smith became Edward Arthur Moonwalk and Alice London Moonwalk, and their father Fiscus Smith became Fiscus Moonwalk. Oh, the clincher was when I finally found that the sister's real name at birth was actually Alice London
Moonwalk Smith. Why all this happened -- and especially how she came to have Moonwalk as a middle name -- I have yet to find out. YDNA testing has not helped at all!
I know that's pretty complex; explaining everything I did to find and confirm the fact that all these people were the same as the others takes an extra dimension or two. A big stroke of luck I had, when it comes to people changing names, was that theirs were distinctive and they retained enough of them, and their birth details, to make them identifiable. While the little info I did have to start with was about the same as what you have -- given names and approx date of birth, and father's given name -- I had that huge stroke of luck, of finding his apparent sister in records, that gave me a triangulation point you don't have. And they had given their father his real given name, while changing his surname.
But the idea is: you are looking for someone who
looks like your person. And then you see whether that person can't be accounted for after a certain point, the point where that person hypothetically became your person.
You, unfortunately, are looking for someone named John born c1862-1864 possibly in Stoke Newington. But things to look for include, first off, people with the same given names born at around the same time and place -- on the assumption that a person is more likely to change their surname, for one of several possible reasons, but keep their given names. That was the first thing in my case: finding the birth of the person with the same given names, born at the right time, and then I found him in a census as a child, and discovered that he disappeared from all records (after death of first wife in 1873) right before my gr-grfather emerged from nowhere (in the 1881 census, once I knew what I was looking for, i.e. place of birth, to confirm it was him).
So the phenomenon is: John Thomas's birth was registered under a different surname, not Bice, and finding him means finding someone who otherwise matches his details but has a different surname. And then tracking that person forward from the point where you find him, whether a birth record or a census, to see whether he has an existence parallel to your John Thomas. If so, he isn't your John Thomas. If you can't find him, you have an hypothesis to work on, and look to see whether there is any connection between anyone in his vicinity (e.g. a mother in the census or on a birth certificate) with the surname Bice.
I hope this hasn't been too much of a headache, but my case is a good example of how these things happen and how "proving" them works.
