The Goring's own history says it hosted Queen Elizabeth II on many occasions and that she was known to drop by for lunch. El País corroborates her dining relationship and 2013 Royal Warrant, but no reviewed source verifies an overnight stay.
Queen Elizabeth II visited and dined at The Goring in London on multiple occasions. The hotel itself says it hosted the late Queen many times and that she was known to drop by for lunch. Professional reporting independently describes her meals at the property and the Royal Warrant she granted for hospitality services.
Source conclusion:
The cited sources confirm dining at the hotel, but not an overnight stay.
