Andy Tait, a forest campaigner, said the campaign had a dual purpose: to stop illegal imports and to ensure that imported timber was accredited as legal by the Forest Stewardship Council.
Greenpeace insists that the only way to end the practice is to cut off demand from countries such as the UK, Europe's biggest importer of Indonesian plywood.
The pressure group said it had succeeded in persuading Jewson to end Indonesian timber imports.
Bovis Lend Lease has also refused to buy wood that is not certified by the Forest Stewardship Council.
Ian Goldsmith, group planning director at Travis Perkins, said: "The audit is about having an influence over supply so we can help make the industry more sustainable."