I think many who have a nice safe & clean job in an office environment (no offence intended to those who do) have a slightly skewed view of some things.
The majority of BAME people looking for work will be nothing like the 'graduates' you're probably used to seeing in and around that sector.
Many probably come from the 'poorer' sectors and, like anyone from a 'working class' background, will be struggling to find anything above minimum wage employment in areas such as factories, hotel work, shops, etc . . in which they, and eastern Europeans, are usually well represented.
If the Gov't and other parties want a higher representation of BAME in roles requiring higher education, they need to make that education available at no cost to the families who can barely afford to live . . . but that then introduces a surge of non BAME into the system too - catch 22 yet again