Mr Cook, opening a Commons debate on next week's summit, said prospective enlargement by six countries would not increase the size of the commission. "Britain recognises the importance of each member state attaches to retaining a seat in the European Commission," he said.
"There is a practical limit to how big the commission can become and remain efficient. That is why all the larger member states are willing to concede their right to a second seat on the commission."
Britain, France and Germany among other states, would be prepared to concede one of their posts in return for getting a guaranteed larger share of the vote in the decision-making Council of Ministers.
The Tories said the loss of one seat would be a "big sacrifice for us to make".