Staff training is one way. The main thing that you may encounter is that people treat services for Black readers as a problem, rather than as an opportunity to make the service better.
It is essential not to go into staff training on this issue by blaming people for what they have said, do say, or have done. Be clear that institutional racism is endemic in English society, but that it’s not acceptable and that it needs to be faced. It’s important to keep your message and approach positive. What is best practice? What is appropriate for this service? What is realistic? What can we change?
If you can create an atmosphere free of blame, then you can promote plain speaking. Ask yourself what is the worst that could happen? It is unlikely you will uncover direct racism in your staff team. Keep your approach professional, not personal. This is about delivering a professional service. In the same way that although as library staff we are all entitled to our own private reading preferences, as professionals we do not impose them on other people. So the library service has a policy and strategy to ensure it is delivered by professional staff to all readers without discrimination.
Be prepared to discuss what ‘Asian’ and ‘Black’ means, and what your authority means by the terms. Decide whether you mean to include Asian in Black literature sections, or not. Have a collection of Black and Asian literature for staff to browse. Use any of the Meet the Books exercises to help them explore the range of work on offer. Agree how staff will check that a percentage of titles by Black writers are included in face on display.
Planning and undertaking a consultation exercise is also a good way to begin, and will begin to show what can practically be done to make changes that really have impact.