Police said a review is now underway after the incident, which would look at current security at the palace.
The break-in is one of the most serious security breaches at the palace since 1982, when Michael Fagan evaded guards to get inside the Queen’s private chambers while she was still in bed.
The 31-year-old spent around 10 minutes talking to the Queen after he climbed over the palace walls and up a drainpipe.
A spokesman for the Metropolitan Police said: “Both men have been bailed to return to a central London police station and enquiries continue.
“A review of the specific circumstances of this incident is being carried out.”