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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Scotland Yard said the male youths will appear in custody at Westminster Magistrates' Court on Saturday.
Windy this weekend with gales across northwestern parts of the UK. Rain spreading southeast.
Greater Manchester Police said "inquiries are ongoing to fully understand the circumstances of the incident."