The inquiry, headed by Sir Martin Moore-Bick, has been criticised since its beginning for being unrepresentative.
Many groups and individuals, including the Justice4Grenfell campaign, have been denied core participant status.
The Grenfell United campaign submitted the petition. It said the inquiry should have people on the panel “with relevant background, expertise, experience and a real understanding of the issues facing those affected”.
The petition has reached over 10,000 signatures, which requires the government to respond to it.
If it reaches over 100,000 it will be considered for debate in parliament.
Kensington and Chelsea council were set to meet on Wednesday evening. The Justice4Grenfell campaign was set to protest outside.