David Lawley Wakelin burst into the inquiry on Monday and accused Mr Blair of being a war criminal.
BBC: Protester enters Leveson court room
Police arrested Mr Lawley Wakelin on suspicion of breach of the peace but later released him without charge.
In an interview with radio station LBC 97.3 FM, Mr Lawley Wakelin said it was "surprisingly easy" to get into the court.
The men's compound team of Chris White, Neil Wakelin and Liam Grimwood took silver in their event after losing to Iran in the gold medal shoot-off.
BBC: SPORT | Other Sport... | British archers scoop two medals
Mr Lawley Wakelin, who made a film called The Alternative Iraq Enquiry, brought proceedings in Court 73 of the Royal Courts of Justice to a halt.
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