Green’s Dictionary of Slang

1. knowledge, importance, pride; thus take the granny off, to humiliate, to ‘bring down a peg’; thus to make dirty.

1859		Hotten Dict. of Modern Sl. etc. 47: GRANNY, importance, knowledge.
1861		(con. 1840s–50s) H. Mayhew London Labour and London Poor I 364/1: A compound of black lead and tallow, to ‘take the granny’ off them as has white ’ands, so as the flat’s shan’t ‘tumble’ to the unworkmanlike appearance of the palms of the ‘lurker’.
1870		Hotten Sl. Dict.

2. a knowledgeable person.

1858		London Standard 19 May 6/2: If you come in [i.e. to prison] again, you know / Your chancellor’s a granny.
1882		Atlanta Constitution 31 Aug. 2/2: Our state is in great trouble and commotion, and he is the ‘granny’ to restore peace and harmony.