>Closer than to the US?

Much closer. It's a unitary state with a monarchy and parliamentary sovereignty, it's highly centralized economically and culturally. It's more European than much of Europe. Post war Germany, republican and decentralized economically is structurally more like the US than Britain. The only reason people in the US tend to identify with Britain is Anglo-Protestant identitarianism.

Britain in reality operates a lot like France or Russia, an overwhelmingly strong capital and grand historical old world nationalism with relatively weak constitutional or formal limits on government.