Speaking as someone who has lived and worked extensibly in all three (US, Britain,"Europe") I would argue that Britain is certainly closer to the rest of Europe than it is to the US.

I live in Sweden now, the organisation I work for is in the Netherlands, I have relatives in Switzerland and in Spain. The way society is structured in all of the EU countries I have visited or lived in are way closer to each other than to the US, including Britain IMHO.