The different levels of risk associated with living in different countries makes it impossible for life insurance policies aimed at UK residents to cover all countries internationally by default.
Some policies will, however, be happy to cover you if you only move to one of a certain small number of countries. Those expats who are not going any further than the European Union are most likely to be in luck and the same goes for many of those moving to the US.
If you are going to a country for which the Foreign Office have issued travel warnings or, worse, which has been declared a war zone then you are likely to need to approach a specialist insurer. There are many policies which specifically exclude deaths as a result of war or political unrest and so even if you could persuade your present insurer to extend coverage, it may not be comprehensive enough for your situation.
It is crucial that when attempting to extend your present cover you inform your insurer several months before moving and you get their agreement in writing to cover you. At the same time, it is also important to remember that the main benefit to getting your present insurer to extend your present coverage is convenience. There is no reason to think that the premiums they offer you or the amount of coverage provided are the best you could get if you were to apply elsewhere. This means that there are often benefits to shopping around.
Moreover, it is generally only possible to extend your coverage if you can give your insurer a firm date for your return. If you are hoping to assume expat status more permanently then you will likely need to find either a British firm which specialises in expat coverage or an international company offering worldwide insurance policies.