My businesses (the 2 businesses that I manage) employ a total of 140people in two different regions. About 12% of my staff are employed at UK Living Wage. I have no problem in getting candidates for these jobs when they are available and we have never applied a 'filtering' system. One region has more ethnic diversity than the other but from the applicants over recent years we have employed white British, Eastern European, South Asian, African, Thai and Philippino. We have never had a single 'black' candidate even though there is a significant proportion of one local population that is black. I have no idea why that is.
From these candidates several of all of the groups listed have have been promoted such that we have senior operational roles and middle management positions filled by an Indian, a HK Chinese, two white South African, a Thai and a Pole. I am sure we are not unique. What has always been evident is that some people just do not want to work. I have had a number of candidates (all groupings) that have come for interview and actually say that they have only come because the benefits office told them to!
Even though I fully accept there is still a minority of stupid racists; to some degree everyone influences their own future and I do not accept skin colour automatically holds anyone back.