Officers were called to Westminster Abbey around 12.30pm today after security guards detained a 41-year-old man.
He was arrested on suspicion of criminal damage and taken to a central London police station where he is in custody, a Metropolitan Police spokesman said.
The portrait, a Ralph Heimans' oil on canvas designed to commemorate the Queen's Diamond Jubilee, had been on display in the Chapter House for a few weeks before it was vandalised with paint.
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The position, posted on the British Monarchy website, pays £16,000 a year for 20 hours a week.
The parents of missing 15-year-old Bristol schoolgirl who is believed to be heading to Syria have urged her to come home.
I think it is fair to say that was the best speech I have seen David Cameron give in the decade I have been reporting on him.