John Joseph NORTH married Elizabeth MARTIN Dec Quarter 1896 at Bedford, so Theobald is not a child of that marriage. (The 1901 census gives the father as John Joseph North, not John Joseph Newton North.)
Since he was registered as NEWTON, it would seem probable that his mother was also a Newton at that time. In 1891 an Elizabeth Newton is with her husband Joseph Newton (from London), and her parents Joseph and Sarah A. Martin in Bedford (RG12/1248 f4 p2). The "where born" column is a mess, an entry has been added, but there is no corresponding data in the rest of the census entry. Elizabeth is probably given as born at Sandy, with siblings born at Moggerhanger which fits reasonably well with the 1901 entry (Blunham).
I can find no evidence of a marriage of Elizabeth Martin to Joseph Newton.
My theory is that the Newtons were not married, but were living as man and wife. Theobald should have been enumerated with them in 1891, but the enumerator accidentally missed him out and started to correct the entry but failed to complete the correction. When the Newtons split up, Elizabeth reverted to her maiden (and still official) name to marry John Joseph North, who brought up Theobald as his own, whereupon Theobald started to use his stepfather's surname. (All other name inconsistencies are just enumerator error.)
