Is Britain culturally closer to America or France/Germany?
I can only give my own experience. I have lived the largest part of my life in the U.S., but I have lived outside the U.S. for significant stints including in the UK. My father ran a large manufacturing facility in Belfast and we also stayed in England for a time.
I have been to the UK more often than any other country except Mexico (land border, what can I say.)
I have also been a lot of places in continental Europe.
I can't tell much difference between people in ALL the places I have been. Most people spend time at work to earn their livelihood. Most people have families at home that they care for deeply and would make great sacrifices for the well being of their families. Most people have a similar idea about what is right and wrong on the big important things like being loyal, honest and trustworthy with friends and family. Most people live in the grey area of their own morality and struggle between selfishness and helping others. When I see a father or mother playing with their kid, feeding them or checking on their education, it is hard to see any significant differences. When I see a family at their child's wedding, they seem the same.
That being said, I personally get on better with Brits than people from the rest of Europe. The jokes they tell and the ways they tease each other are very familiar. If a Brit invites me to a social event, I am probably going to have a good time and not get stuck in some depressing philosophical or political discussion.
When I am travelling around the world, I feel like I am already home when I stop off in London. I can't say the same about France or Germany. We grew up reading the same books in school, watching at least some of the same movies and TV shows and hearing the same stories. Those things aren't terribly important, but they do lead to a certain comfort level.
I am sure that an average Brit has more in common politically with a French or German person than a right leaning American from the South, but that is just politics, the thing that artificially divides us. If politics are an overriding factor in your life, we are very different, if not, we are very similar. From where I stand, talking about guns, politics or religion with people is like looking for conflict. I do my best to blow right past those topics when they come up without giving any clue to where I stand on an issue, if I stand someplace on an issue at all.