The man in blond wig, suit jacket and tie scaled the tower, which is covered in scaffolding for repairs, and unfurled banners reading "No pride on a dead planet" and "Citizens Assembly".
The Press Association news agency identified him as 43-year-old tree surgeon Ben Atkinson. He posted a Facebook comment urging Johnson to convene a citizens' assembly.
Extinction Rebellion has staged two weeks of demonstrations in London calling for stronger action against climate change.
In one event, protesters who stopped a subway train clashed with angry commuters. The group apologized Friday for the disruption, saying "we don't do this out of malice, we do it because we are scared and we care."
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