Exasperating uneducated woman stops one perhaps reading books (8)
I believe the answer is:
irritant
'exasperating' is the definition.
'uneducated woman stops one perhaps reading books' is the wordplay.
'uneducated woman' becomes 'rita' (character from the play and film Educating Rita).
'stops' means one lot of letters goes inside another.
'one' becomes 'i' (Roman numeral).
'perhaps reading' becomes 'r' (one of the three R's of education).
'books' becomes 'nt' (New Testament).
'i'+'r'+'nt'='irnt'
'rita' going inside 'irnt' is 'IRRITANT'.
(Other definitions for irritant that I've seen before include "Annoying thing" , "Trouble" , "Something that annoys, a nuisance" , "Source of continual annoyance" , "causing annoyance" .)