The work hard mentality I think owes a lot to religious beliefs - the Methodist ideals of working hard and idleness being sinful still persist in the UK in areas which Methodism was strongest. These areas tend to be old mining areas. There are multiple similarities between voting patterns in the UK and US in line with this too for a number of reasons.
And yes, being a settler would bring a certain mentality. You couldn't rely on anyone else. You survived or you died. Substance living really stopped in the UK much earlier than it did in the US because of urbanisation.
The reality of the American Dream has largely died and has been replaced by a new class system as the country has matured and an establishment formed. It's meant opportunities have shrunk. But many haven't quite grasped this - partly because if they acknowledge that it undermines certain parts of this inner sense of national pride and identity.
Meanwhile the UK diverged in its mindset due to it's lived experience during WWII and how the public and state worked together to win the war (the reality is slightly different to this myth - but it's one that's been imprinted on our national identity).
If you think about Trump mantras like America First in the context of areas which haven't changed much in 200 years in makeup, settling the land, isolation and looking after your own mentalities it actually makes a lot more sense. These are concepts Europeans really struggle with because it's wildly different to their experiences over the last 100 years and how Europe has developed.
The whole thing is fascinating. You do have to look at how countries have developed and key moments and lifestyle to get national identities better.