Most of these rules as they apply to consumers have been incorporated into Consumer Insurance (Disclosure and Representations) Act 2012
http://www.legislation.gov.uk/ukpga/2012/6/contents/enacted
Insurance companies are regulated by the FCA. They are subject to certain statutory duties and if they breach those duties you can sue them in the County Court.
In addition to being obliged to treat you fairly under COBS, insurance companies are not allowed to refuse to honour your claim for some reason which does not affect the risk.
A common requirement is that you notify the insurers within a certain number of days. Mobile phone insurers very commonly refuse to pay out if you haven't told them within 48 hours.
Motor insurers may insist that you have your repairs carried out at a designated garage. This is an unlawful requirement.
These are violations of ICOBS rule 8.1.2 - even though insurers do this all the time.
Don't forget that insurers make their money by NOT paying out - not by paying out.
