The actor won the award on Sunday (19 September) for his portrayal of Prince Charles in Netflix’s royal drama The Crown.
Josh O’Connor accidentally clocked himself in the head with his Emmy trophy at the weekend, while mid-embrace with a fellow guest.
Anderson was asked by a reporter at the press conference whether she had spoken to Thatcher about her depiction of the politician.
The Crown won a total of 11 Emmys last weekend, with Gillian Anderson also taking home a prize for her portrayal of Margaret Thatcher, and Olivia Colman for her role as Queen Elizabeth II.