As Eddie has said, you can complain to the Insurance Ombudsman, their address will be included in your insurance documentation, but you cannot do this until you have exhausted the company's complaints procedure.
The policy documentation should include details of who you should address your complaint to. Do this in writing. They then have 5 working days from receipt to acknowledge your complaint, followed by an 8 week window to investigate and supply you with their response. These time periods are set by the Financial Conduct Authority in the Insurance Conduct of Business rules and regulations, which unfortunately won't necessarily help to speed up the payment of your claim.