Firstly, you could try to resolve the matter directly with the organisation involved. If this is a hotel, for example, you could write to the manager, and possibly to their head office. If you have been discriminated against by an NHS service, you will need to use the NHS complaints procedure.
If there is a relevant regulatory body, you could also get in touch with them. For example, you could get in touch with the local tourist board for a hotel, or the Financial Services Ombudsman if you are complaining about a financial service provider.
If you're unable to resolve the matter in this way, you could pursue a case in the county court in England and Wales or the sheriff court in Scotland. Where discrimination is found to have taken place, the court can award financial compensation.