Daewoo takes a belting

DIFFICULT to apportion blame here. When they talk about the belts, were they talking about the cam timing belt or the external belts? The cam belt needs to be replaced at the carmaker's service recommendation. If that wasn't done, then you probably have a claim. If it was changed and it subsequently broke, you probably don't have a claim. You need to check your paperwork and see if it refers to a manufacturer's logbook service. You should also check for a guarantee, because most service people will back their work with a warranty.