Lord Patten has refused to appear before the European Scrutiny Committee and its Tory arch-Eurosceptic chair Bill Cash prompting accusations he is abusing his position as a Lord.
Commons Leader Andrew Lansley said he would raise the issue of accountability with the BBC as Mr Bercow stressed that no-one is too senior to be above scrutiny from Parliament.
Lord Patten - a former EU commissioner - has three times rebuffed requests from the cross-party panel of MPs and peers to appear before it.The committee found "serious questions need to be answered about how EU issues in general and scrutiny in particular are covered".
Mr Bercow said: "Anybody who's invited to appear before a committee in this House should do so. No-one, no matter how senior should imagine him or herself above such scrutiny."