I don't think it works that way and I don't think anyone thinks it does. In the UK if an MP (Member of paliament) dies or resigns then there is an election to replace them.. when a PM (Prime Minister) dies or resigns it tends to be passed on in that the party/cabinet elect a new representative. Personally I'd rather they called a new election but I am guessing that general elections (aka national ones) are expensive and hassle.