Does Britain have consent of the governed?

Yes, Britain does have the consent of the governed. The United Kingdom is a constitutional monarchy, which means that the monarch is head of state, but the actual power lies with the Prime Minister and the Parliament. The Prime Minister is elected by the House of Commons, which is made up of elected representatives of the people. Therefore, the government is accountable to the people, and the people have the right to vote for or against the government in elections.