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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Mr Kim has made two recent visits to China.
The study looked at the development of 422 children over the course of eight years.
The president said they will come into force if China refuses to change its practices.