Just checked again and unfortunately English DC's of 1933 appear not to give parent's names like the Scottish and New South Wales DC's, it just might have give a clue.
I think Col has found something very interesting with the BC of "Male" Wood in 1901, I would get that BC as it is worth having a look, one name must be there, the informant. Go to freebmd.org.uk/search , you can pay by Credit Card and they post to you.
Of course there is always a chance it is a still birth and therefore un-named child.
Did the 1925 WC to Lily Entwistle show Theodore's adoptive parents /