"One window from the guardroom opened up and when a soldier saw what was going on he told his mates - and lots of windows opened up," witness Mark Robinson told The Sun newspaper.
"The couple did not care who was looking and just kept going as if they were in their own bedroom."
Japanese tourists filmed the couple, who only stopped when police officers arrived on the scene, witnesses said.
Thames Valley Police said the man and woman were arrested and given a written warning about outraging public decency.
The queen was in the castle at the time, but her office declined Friday to comment about what had happened.
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