In any case, excluding all the rivers etc, what is the estimate?
It's hard to say, because you have got to factor in the whole thing about "The places where people generally want to live are the heavily built up places."
we are more similar than you think. In fact, lots of the same ideas about immigration floating around in both countries.
Sure, but there some differences in the starting conditions.
The US is thinly populated for a start, whereas the UK is very densely populated--and if you break us down into our components, England is actually the most densely packed in Europe, and close to the top of the world. (The Netherlands used to be more densely populated, but we have overtaken them.)
The majority population in the US (white culturally-Christian people) are the descendants of invaders, and the US has always been a multicultural country. The UK by contrast is a country where the majority population is also the indigenous population, and that means that the immigration debate "feels" different right from the start to many people.
The US has hardly any welfare state to protect. The UK does. This makes the debate more complicated and it also means that is is not a simple left/right, red/blue debate. For a number of complex reasons, there tends to be a trade-off between generous welfare states and generous immigration policies in the long run (which is part of the reason why the Swedes are struggling desperately right now).
The majority of immigrants into the US are of Latin heritage, and integration is mostly pretty good--certainly compared to Europe. Relatively few immigrants to the US are Muslim. Immigration is inherently more complicated in Europe, partly because we tend to get more immigrants from extremely poor and "difficult" parts of the world (for historical and geographical reasons) and partly because as I said, there is a tension between immigration and the welfare state. We are also far more secular than the States, and the religiosity of many Muslim immigrants does not fit neatly into our societies.