To be fair, the US attitude towards assimilation and general “melting pot” philosophy does tend to help immigrants feel welcome and encourage them to take part in the overall culture. Relatively free transfer of land, the ability to expand, and the (perhaps mostly imagined) potential for upward mobility int he US culture helps a LOT.
In an Old-World town where the natives have lived for many hundreds if not thousands of years, where the local corner shop has stayed under the control of the same family for multiple generations, and where the expectation that a son will absolutely follow in his father’s footsteps and take over the family business… then the presence of a new “other” will not be anywhere near as welcome as in the US. An immigrant in that environment will have a far, far harder time trying to find a niche in the prevailing culture… and thus may be left with little choice but to retain their own culture or start a - necessarily insular - enclave.
Cities are probably a little different. I imagine that a new immigrant landing in London as opposed to a village in the Midlands would have an easier time.
And although I am an advocate for immigration, I will play Devil’s Advocate for some of @draxen 's points.
First, a large influx of people from a different culture WILL erode the overall influence of the existing culture. That’s just a a thing that happens. In the US we tend to be alarmed (gentrification!) by this or shrug at it depending on whether the existing culture is a minority one overall or not.
Take a fairly neutral case from US history - the city of St. Louis.
First off, the initial displacement of the Ottowa culture is bad, because it was pretty much done illegally through theft of the land and over the objections of the rightful regime. So let’s not talk about that part.
For the first hundred years or so of the city’s existence, it was French (even though for much of that time it was technically in Spanish territory). If you drive through St. Louis, many of the place-names (as opposed to the streets) are French: LaSalle, Gravois, DeBaliviere, etc. Many of the surrounding townships like Florissant have French names. French was the primary spoken language.
In the 1840s, German immigrants began to arrive in the area in large numbers. The city population ballooned from 20K to 80K in just a decade.
And the existing, French-English culture was pretty much washed away. It didn’t disappear, but it was watered down massively. German became dominant tongue (and would remain so until the US entered WWI), and Germanic attitudes towards work and slavery prevailed against the previous pro-slavery stance.
Many of the French-English residents of the city in the 1840s warned that the influx of “Hunnish” immigrants would supplant their culture and way of life. And what they predicted came to pass.
Was anything precious lost with that culture? Tough to say. The Germanic character of the city is now held up as a point of pride… as is the previous French “golden age”… and as is the current majority African-American culture that has pushed the previous culture out into the suburbs.
This got kind of long I guess. The point is that immigrants’ cultures can and do water down or completely replace existing cultures if the newcomers arrive in very significant numbers. In the US we don’t tend to care too much, because cultural change has been expected and often welcomed throughout our history and for the most part we don’t consider our culture as anything precious (as opposed to our philosophy, which we cherish). But things are different in places where the culture has deeper roots.
