That is true, but changed over time with the changing local political climate. Back in 2004 Angela Merkel was still strictly right-wing anti-immigration, later she drifted more and more left and pro-immigration.
2004 Merkel also wasn't in power. And I think it's relevant, because IMHO the years after 2004 lead to the shift in British public opinion that lead to immigration restrictions becoming such a big topic, and pushing politics towards the referendum.