I think he has been very selective with the use of statistics. Yes, there are very few black British students of Caribbean origin at Oxford and Cambridge and that is scandalous (there are plenty of students of a wide variety of other ethnic origins, however).
But, as the article mentions, only 292 black students in the whole country achieved 3 A-grades at A-level, which is realistically what you need to get into Oxford or Cambridge. About 30,000 people apply to Oxford every year, most of whom have 3 As at A-level - and most of them don't get in either. There are lots of people with 3 As who don't even apply to Oxbridge.
Yes, I'm sure the universities could be doing more to encourage black students to apply (though there are outreach programmes to inner city comprehensives etc and have been for at least 25 years), but the real scandal is with the school system that leads to serious underachievement for so many black (and other ethnicity) children.
I really don't see how universities can fairly be expected to compensate at university entrance level for 14 years of poor education, but because Oxford and Cambridge are already seen as elitist, they make an easy scapegoat. If they started some kind of affirmative action programme for black students that would immediately cause an outcry because it would not be fair to every other under-represented and under-achieving group, like working class white boys.
And of course the problem of underachievement and low aspirations in schools is compounded by the attitudes of teachers and families who discourage bright students from applying to Oxbridge because of outdated beliefs that it is 'just for posh people', which just perpetuates the problem.