British throne given to primarily dotty family (5)
I believe the answer is:
'family' is the definition.
(I've seen this in another clue)
'british throne given to primarily dotty' is the wordplay.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'throne' becomes 'loo' (both can mean a toilet).
'given to' is a charade indicator (letters next to each other).
'primarily' says to take the initial letters.
The initial letter of 'dotty' is 'd'.
(Other definitions for blood that I've seen before include "Gore" , "Kinship; temperament" , "Become the duty of" , "Vein filler" , "Oxygenating fluid" .)