You're misinterpreting the first table. The percentages do not add up to 100% in any column; only within one row does it add up.

So, within all people identified as Black, 31% are in the lowest quintile.

Also, within all people identified as White, 18% are in the lowest quintile.

If you subdivide White into White British and White other, then you still get about the same thing (18% for the former, 19% for the latter).

You can't add 18%+18%+19% because they aren't independent groups! They're the same people, just subdivided in different ways.

So the table really just says: 31% of blacks are in lowest income quintile of the country as a whole. 18% of whites are.

Furthermore, your logic about percentages is a bit strained. Suppose, hypothetically, that you throw every single Maltese person in jail just because you decide you don't like Maltese people. 100% of Maltese are in jail. But it's only 25,000 people or so--so, hey, do we not worry about this? Well over twice as many non-Maltese white people are in jail in Britain. So, yeah, no real problem here?

But of course there is a problem! There could not be a bigger problem with jailing Maltese people. They are literally all in jail!!

So you have to look at both. If lots of people of one numerous group in jail, you certainly don't want to completely neglect their experience. But on the other hand, percentages direct your attention to where there's a problem.

Noticing that there is a problem doesn't tell you the cause, nor does it tell you why. For instance, if everyone of Maltese birth came to the U.K. to try to overthrow it, and they were all caught, and thrown in jail, that would be a very different scenario from the U.K. deciding prejudicially to lock up everyone of Maltese birth for no reason. Same percentages: they're all in jail. Completely different reasoning.

So, the disparity in percentage in prison is not something to dismiss lightly. It could be a sign of something really amiss, really unfair.

Now, you can make a point about prison numbers vs. income numbers to deal with the issue of class. The percentile prison numbers look bad but what are the causes? Is it explained by class (e.g. income quintile)? If there is a residual disparity in imprisonment, can we figure out why? And if it is due to class, why is there a class disparity? Is it because of negative stereotypes or unequal treatment of blacks, or because of historical accident, or because of country of origin coupled with lack of social mobility, or because of different subcultures, or something else?

Is the answer the same with various ethnic groups (e.g. why the huge class difference between Indian and Bangladeshi populations?).

Anyway, I'm afraid the treatment of the statistics needs to be done in a more careful way than this to really start uncovering whether or not there are problems, and what the problems are.

Maybe the smart thing to do is decide that talking about "white privilege" is harmful overall, and we should each just get on with improving ourselves and helping improving things for those we're close to, and forget about glomping things together by race. Maybe that isn't the smart thing to do. But regardless, if we're going to do this analysis, it deserves a rather painstakingly careful treatment because, alas, things are complicated.

(Apologies to people of Maltese descent--I don't mean to imply anything. The Maltese-born population is just small enough to serve as a good example of the logic.)