.I'd say the biggest difference is size, I imagine in America you'd feel more isolated, as you could quite easily live your life in 1 state, whereas in England you'll end up seeing other areas of the country in your life.
Demographically, I'd say the biggest difference is that where America has a huge Latino population, we have a huge South Asian population. Black people here also tend to be West Indian, often going back only 1 or 2 generations, whereas African Americans often go back for generations.
America has a huge gun culture, in turn Britain has a large knife culture. Britain also has a huge fighting culture which goes back centuries.
I'm sure it's the same in America, but in places like London and Birmingham, the urban slang can be almost incomprehensible to people not familiar. There are kids in the big cities who's slang is more similar to Jamaican Patois than English.
I'm not sure if America has them, but in Britain we have loads of Irish Gypsies, or Pikeys. These are without a doubt the most hated communities in the country, as nearly everyone views them as dishonest thieves. They're notorious for their bare knuckle boxing matches in the country side.
Britain has a huge rave culture, not what it was but I'd say it's still more popular than in America. Various drugs like MDMA and ketamine are hugely popular here because of that.
Americans seem to be obsessed with coffee, whereas the British seem to prefer tea.
We have no real wilderness like America, sure we have woods and stuff, but no where near on Americas scale.
A fairly British phenomenon seems to be postcode wars, these have died down now but a few years ago there was a craze of inner city teens stabbing and beating each other over their postcodes. Several kids died because they lived in a different estate from their attacker.
There's also a difference in our mentalities, Americans seem to be loud, in your face, confident and patriotic, whereas Brits are hard, grim, dry witted and reserved.
These are just my observations.