The position of UK Prime minister is very different from that of a head of state.. He/She is not there for a fixed term for one thing. He could be replaced mid-term and can be a member of the House of Lords.. in which case wouldn't be dependant on any election result. The monarch will summon the person most likely to command a majority in the Commons... which may not be the leader of the largest party in some circumstances. During an election the out-going prime minister remains in office until his replacement is appointed ... even though at that point he is not technically an MP.