In addition to the idioms beginning with not

• not a bad sort
• not a bit
• not able
• not about to
• not a Chinaman's chance
• not a hope in hell
• not a leg to stand on
• not a living soul
• not all it's cracked up to be
• not all that
• not all there
• not anything like
• not at all
• not bad
• not bat an eye
• not be caught dead
• not born yesterday
• not breathe a word
• not built that way
• not by a long shot
• not by any means
• not cricket
• not done
• not enough room to swing a cat
• not feel oneself
• not for all the tea in China
• not for a moment
• not for love or money
• not give a damn
• not give someone the time of day
• not half bad
• not have a bean
• not have a clue
• not have an earthly chance
• not have anything on
• not have it
• not have one's heart in it
• not have the heart to
• not having any
• not hurt a fly
• not if one can help it
• not if you paid me
• not in the least
• not know beans
• not know enough to come in out of the rain
• not know someone from Adam
• not know where to turn
• not know whether one is coming or going
• not let the grass grow under one's feet
• not lift a finger
• not miss a trick
• not move a muscle
• not my cup of tea
• not one iota
• not one's day, this is
• not oneself
• not on your life
• not open one's mouth
• not put something past someone
• not right in the head
• not see beyond one's nose
• not suffer fools gladly
• not take no for answer
• not the half of it
• not the only fish in the sea
• not think much of
• not to be sneezed at
• not to mention
• not touch with a ten-foot pole
• not to worry
• not turn a hair
• not up to
• not worth a damn