Euphemia is probably not his mother - I found a 1878 marriage for her and Samuel.
Possibly Samuel Greig m. Hannah Smith in 1853 Newington district, Hannah Greig d. 1874 aged 41, Lambeth district.
In 1871 they are listed as "Grey". John A. B., aged 1.
There is also a brother Robert B, whose middle name is Bennington from freebmd.
So plenty of possibilities here - he could have had family in Scotland on his father's side, he could have emigrated, he could have changed his name. If you trace his brothers and sisters you might find one who emigrated and then you can look to see if John followed them. Or if any 'niece' 'nephew' 'grandson' 'granddaughter' 'cousin' etc. turns up with other parts of the family who might be one of John's children.