Update: The ONS have actually published updated estimates for the population by country of origin here. I can't open zip folders right now, so if anyone wants to open it and see where the new immigration since the last census has come from. feel free to paste it into my comments.
In the comments to my previous it is pointed out that the government is claiming that the '1 in 9' statisitic is misleading because many of the foreign born are actually people born to British forces families stationed overseas.
This seems implausible to me. Here is a list of the top 25 countries of birth for residents of the UK according to the 2001 census (rounded to the nearest 1000):
Great Britain: 53,923,000
South Africa: 141,000
Hong Kong: 96,000
Sri Lanka: 68,000
New Zealand: 58,000
Of those countries it is fair to say that a fairly large proportion of the German and Cypriot births are from British forces overseas, as may smaller proportions of those from Kenya, Hong Kong and Canada, but it is clear that they only make up a very small percentage of all those born overseas.
Mind you the raw statistics also show that a considerable number of those not born here are from other reasonably wealthy english speaking countries, some of which are cultural off shoots of Britain in the first place, which is probably worth emphasisising.