It's a civil matter. Cases of (alleged) discrimination, other than those related to employment, are heard before the county courts:
http://www.cre.gov.uk/legal/complaint.html
If the police were asked to attend an incident where racial discrimination was alleged, they might choose to do so in order to prevent a possible breach of the peace. If they did attend, it's likely that the officers would remind the service provider of the provisions of the the law. However, there is no actual obligation upon the police to attend an incident or to advise the service provider about the law. Further, neither the police nor the Crown Prosecution Service can take any direct action in relation to allegations of racial discrimination.
It's extremely difficult to prove an allegation of racial discrimination based upon a single incident. It's
not illegal to refuse to serve a black man. It's only illegal to refuse to serve a man
because he is black. If the service provider declines to give a reason for refusing service, proving discrimination only really becomes possible if his reasons become clear through repeated breaches of the legislation.
Chris