I reject the assumption made in the broadcast that all objections to mixed-race marriage are rooted in outdated attitudes, bigotry or down-right racism.
Most human diversity (racial, cultural and linguistic) are the result of human populations in the past having been isolated. Modern transportation and mass migration have removed the geographical barriers; removing the taboo of inter-racial and inter-cultural marriage will have the effect of destroying the very diversity that the proponents of multi-racial/multi-cultural society are so fond of extolling.
A certain amount of racial and cultural mixing increases human diversity, for sure, and we are the richer for it, but if they become the norm, because the taboos which discourage them are discredited (as "racist" for example), as this broadcast implies they should, in 100 - 200 years time Britain's native and immigrant populations will have merged into a more-or-less homogenous population of mixed race and hybrid culture.
If I myself were of mixed race, or had children who were, perhaps that is what I'd want, as a means of overcoming the dominance of the native white population, but I'm not, so I don't. Besides which, I love and want to retain racial and cultural diversity. To this end, having removed the geographical barriers, we need to cultivate (not vilify), in a humane and civilised fashion, cultural and political ones.
Such barriers should not be impregnable, of course, but sufficient to maintain diversity; nor should they be imposed, but individuals free to decide for themselves. However, individual communities must also be free to decide the conditions of membership. If a community of black people doesn't want any white members that is perfectly legitimate, and visa versa. So if a black and white couple wish to marry and both their communities reject them, they will have to find another communitiy to live in. There is no reason, however, why the rejection should be hostile or total, but every reason why it should not be. The attitude of their communities is not "racist", but necessary to preserve their racial integrity and the racial diversity of society at large. If you don't want these things (perhaps because you mistakenly believe wanting them to be "racist"), no one is forcing them on you; but please, don't you try forcing others to join you on the road to racial homogenization.
Link to BBC Radio 4 website: http://www.bbc.co.uk/radio4/factual/pip/92te8/