European Commission President Jose Manuel Barroso has been voted Britain's most powerful man in a BBC poll.
Mr Barroso came ahead of the likes of Mr Blair and Mr Brown
Mr Barroso, who is unelected, received 22% of the vote in the BBC Radio 4 shortlist which included Rupert Murdoch and internet search engine Google.
Prime Minister Tony Blair, Gordon Brown and Parliament were deemed less influential but still made the top 10.
BBC political editor Nick Robinson says voters may be using the poll to say Europe has too much power.
Mr Blair got 7% and the chancellor 4%, which was less than the 10% polled by Cabinet Secretary and chief civil servant Sir Gus O'Donnell.
Who Runs Britain? poll
1. Jose Manuel Barroso - 22%
2. Rupert Murdoch - 15%
3. Parliament - 14%
4. The British People - 12%
5. Gus O'Donnell - 10%
6. Terry Leahy - 7%
7. Tony Blair - 7%
8. Google - 6%
9. Gordon Brown - 4%
10. Shami Chakrabarti - 4%
Tesco chief executive Sir Terry Leahy received 7% and Shami Chakrabarti, director of civil rights group Liberty and the only woman in the top 10, got 4%.
The European Commission is the EU's executive body and the only EU institution that can propose legislation.
That is where the commission has its power, Nick Robinson says.
Commenting on the Who Runs Britain? poll, Roger Knapman, leader of the UK Independence Party, congratulated those who voted for Mr Barroso.
"Of course it is the only chance you'll get to vote for him or for that matter against him," he said.
"He is now a bureaucrat perceived as the most important man in this country and that is quite shocking."
But former Europe Minister Dennis McShane said it was "an urban myth" to suggest that Britain's laws were decided by Europe.