The correct part of your analysis is that special help for people who are disadvantaged, homeless etc should not be focussed on ethnic minorities since in absolute numbers there are more white people in this category. So this type of help should be focussed on the situation only.

However, this does not mean that there is not evidence of discrimination or some sort of unequal outcome due to cultural factors or assumptions being made.

Looking at the income table it is unsuprising that the quintile data for whites is almost exactly 20% for each quintile. This is because the huge majority the white population has means that their numbers pretty much determine the quintile boundaries.

So we can see that blacks are disadvantaged with a larger proportion in the lowest quintile and a smaller in the highest.

Interestingly, Chinese and Indians have a higher population in the top quintile than whites.

Pakistanis are the most disadvantaged but are also more recent immigrants.

So its a complex mixed bag as usual.