The Human Genetics Commission intends to study the use of family history in underwriting, regarding it as genetic information in a broad sense. We survey the developments in genetics and insurance that led up to this decision. We propose a model for studying the possible costs of adverse selection in the mortgage-related life insurance market (which is important in the United Kingdom) with and without moratoria on the use of family history. We consider both level and decreasing term assurances, finding that the cost of adverse selection is slightly higher for the latter. Several assumptions about mutation penetrance, incidence of additional mortality, prevalence of genetic testing and insurance-buying behaviour are considered. Overall we conclude that: (a) a moratorium on genetic test results alone will lead to negligible adverse selection costs; while (b) a moratorium extended to family history will lead to premium increases just by redefining underwriting classes, with adverse selection being possible as well, but only in extreme circumstances would all premium increases be likely to exceed about 10%. However, we give examples in a model of a smaller life insurance market that show that our benign conclusions might not apply more generally.