The CPS said no prosecution could be brought because the "evidential test" had not been met.
Alexander Lewis-Ranwell is accused of three murders and will appear in Exeter Crown Court on Monday.
It is the second time in two weeks the philosopher's grave has been attacked in Highgate Cemetery.
"Why we skipped school for a climate protest"
Why have efforts to raise HMS Victory stalled?
Showcasing the best images sent to us from around England.
What next for Donald Campbell's record-breaker?
In London for 1000 years and they have billions in assets
Celebrations are held to mark Chinese New Year
Premier League champions Manchester City travel to League Two Newport - follow in-play clips, radio & text.
An in depth look at Frank Sinatra
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