OK, last try to show you some sense.
Rewind 100 years, when there were very few immigrants in this country; the only non-indigenous people who lived in Britain in significant numbers were the Jews, who were relatively recent arrivals, non-European in genetic terms, and had remained a distinctive population (i.e. had not interbred to any notable extent).
Then you have the Britons. There are small differences between the Scots, the Welsh, and the English, and also small differences between regions such as East Anglia and Cornwall, reflecting historic population flows; but essentially Britain is genetically a pretty homogeneous place.
Now taking a random Briton, and looking at his genes, having the benefit of present day genetics we would be able to infer the geographic ancestry of this individual within a few hundred kilometres; i.e. we could put him on a map like the one on this page
http://dienekes.blogspot.com/2008/09/geography-and-genetic-structure-in.htmlAnd adding in more individuals we would see that the Britons are a distinctively Northern European population, and are distinctive to a certain extent even within that race.
There is nothing very messy about this at all. Britons are I believe descended primarily from the ancient ice age populations that inhabited Britain, but we have had genetic input (which tends to be exaggerated) primarily from very closely related populations like the Anglo-Saxons, the Normans etc.
Note: These are not Pakistanis, Chinese and Nigerians - they are people who were scarcely different to the existing Britons in the first place.
Whatever our population history though, the very fact that we plot onto a PC map (such as the one I linked to) in the manner that we do indicates that there is a strong racial meaning to being British - talk of Anglo-Saxon ancestry etc. is basically meaningless, when we are presented with such direct genetic information.
So when I say near-complete British ancestry, I mean having ancestry that is of these Britons, these people who could trace their ancestry back many centuries in Britain.
Although this particular judgement is a little arbitrary (so what, most things in life have to be) I would also say that e.g. a 1/4 German, 3/4 Briton (where a Briton is one of those British individuals, who plots in the British area of the PC map, and can trace his ancestry back as being from the same background of ancient Britons and historic contribution of Danes, Anglo-Saxons etc. that is shared with the other Britons) is an indigenous Briton, and so is an 1/8 Russian 7/8 Briton, and so on and so forth.
If you object to the idea of indigneous Britons, then perhaps you should stop using the word indigenous at all, because in real life no population can claim to be an absolute Platonic race that has always inhabited a given territory and has never mixed with surrounding populations for many thousand of years. The word indigenous is very useful and meaningful, and there simply is no reason to discard it, or the word race, just because it doesn't satisfy some absurdly rigorous criteria that you want to invent.
For example, the category 'age' is pretty unclear/arbitrary; who is old and who is young, is there any clear and consistent demarcation between old and young? No. But clearly this does not mean that we should throw the word 'age' out of the window and let a 50-year-old pervert have sex with an 8-year-old. The only person who would suggest such a thing would be the paedophile himself - someone who had an ulterior motive for dispensing with the category 'age'.
By the way, my definition of race in this context would be 'a somewhat distinct biological entity emerging as a cluster of similarity from the genetic continuum'.