German chancellor Angela Merkel met the Queen at Buckingham Palace this afternoon.
"You've had a very busy day," the Queen said.
"Yes but it's my duty to have busy days," Mrs Merkel replied.
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The singer had been tweeting in support of migrants when she was bombarded with abusive messages.
Ministers are reportedly considering plans in a bid to lower inward migration.
In a tweet on Saturday, the US president didn't give a reason for his absence but said he wished"everyone well and have a great evening".