Some practical points:
Contact the local register office to see if the death has been registered:
http://maps.direct.go...ction.do?ref=grolight
(If no relative comes forward, the registrar is permitted to allow someone else, such as a hospital official, to register the death).
Contact the hospital to see if they have been contacted by a funeral director (and, obviously, ask who that director is).
Remember that nobody is ever OBLIGED to arrange a funeral. Your cousin is entitled to refuse to do so (but, clearly, it would help you if she told you whether she intended to do so or not).
Remember also that anyone CAN arrange a funeral. (A complete stranger can arrange someone's funeral, without any consultation with the relatives and with complete disregard for the wishes of those relatives or of the deceased person. He who pay the piper calls the tune).
Further remember that, in most circumstances, the costs of a funeral can be met from the estate of the deceased person. (So, if your uncle left money or property, you can probably arrange the funeral - if necessary- but claim against his estate).
All of the foregoing relates to the practical (and legal) situation. However your question clearly also addresses more personal issues. You need to recognise that the parent-child bond is extremely strong in some cases but almost (or totally) non-existent in others. Some people feel strongly about 'family ties', whereas others (like me) couldn't care less about them.
You clearly had a strong bond between you and your father but you shouldn't assume that such a bond necessarily existed between your cousin and her father. (I only attended my parents' funerals because 'of appearances'. I couldn't have actually cared less about them. I've deliberately removed the markers from their graves. Similarly, my will makes it clear that no member of my family will get a penny of my money, and that I want to be cremated with nobody present).
I'd rather have an honest cousin who freely admitted "I couldn't care less about my father's funeral" than a hypocritical one who bothered to arrange it.
Chris