Well here's a turn up for the books, from the pages of Hansard:
David TC Davies: To ask the Secretary of State for Energy and Climate Change, whether members of the Climate Change Committee are permitted to have financial interests in businesses which might be affected by energy and climate change policy.
Amber Rudd: The Government and the Committee on Climate Change takes very seriously the need to ensure that board members have no conflicts in fulfilling their public duties. When appointing to the board, the Government follows Cabinet Office guidance about making public appointments that sets out the rules and transparency requirements which must be satisfied before public appointments can be made.
I wonder if a follow up question along the lines of "What steps would be taken against committee members who were found to have made false statements about their business interests during the recruitment process?" might be interesting.