1. The first thing you should do is check your policy document (make sure you always have one when you take out insurance). Double check the documents to see if you gave the insurance company the right details when you bought the insurance. Spot the areas that show that you are covered. Gather up any other documents and previous communications with your insurance company that includes covernotes, emails, receipts etc. Get witnesses to back you if you have to.
2. After you take a look at your policy documents and you are sure you were covered, make contact with the claims department of your insurance company preferably through a formal letter or email. In the letter clearly state your complaint and explain why you think your claim should not have been rejected. Attach all the evidence to support your case. Mention that you would like them to reconsider your claim rejection. Submit your letter and make sure you have the company's representative sign a copy that you will keep for your own record.
3. If your insurance company does not change thier original decision to reject your claim, ask for a simple document outlining their reasons. Study it and compare with your own notes. If you still feel your claim was unfairly rejected, you can get assistance from Insurance and Pensions Commision (IPEC) who will act as an arbitrator. Submit all your documents and correspondence from your insurance company. They will weigh up both arguments and come up with a fair outcome. I am pretty sure it is within their power to order an insurance company to pay a claim if they deem your argument factual and correct. However, you should also not raise your hopes as you might be wrong.
Finally you should know it is common for insurance companies to reject a claim if they feel it is out of their prescribed cover. However, because their staff are human sometimes they make mistakes. A simple filing error or misinterpretation of your policy by the insurance company could lead to your claim getting rejected but you shouldn't bear your own loss because of it. If you've had your claim rejected please share your story in the comments.