Karl, although Germany's attempts are admirable, they could take 10 million more people before their population density was the same as the UK's ... and, more noteworthy in the circumstances, they could take 57 million more people before their population density matched England's.
I appreciate that Germany is a bit more mountainous than England, but I think this sets the context for why the English are complaining about migration into the UK. It's crowded enough already. And, as you rightly point out, Germany is only next best - if you look at France, Italy, Greece, Spain and Ireland, they're way behind.
Now, when you take into account what most people who are against migration give as their reasons for being against it ... the increased instant need for housing, healthcare, education, policing and other infrastructure, as well as benefits of course, then you can't ignore the fact that we are already highly populated and not really in need of more people, especially when compared to other European countries.
This is why I believe that some kind of compromise has to be found by the EU on the migration issue. I think there's a strong chance that England, and thereby the UK, will vote to leave the EU if nothing is given.