I don't know if you're from the UK or not, but I'll assume for the moment that you're not... In the UK system, you vote for members of parliament (MP for short)

I don't know if you're from the UK or not, but I'll assume for the moment that you're not... In the UK system, you vote for members of parliament (MP for short) that represent your local area. The majority of MPs have party affiliations, so in principal you vote based on both the local candidate and the party that you want to rule the country (in practice many people know diddly squat about their local MP and vote purely on party affiliation). So long as a party reaches past a set number of MPs in order to reach a parliamentary majority, the leader of that party becomes the prime minister. In principal, as people are voting for the best combination of MP candidate and party that suits them, there's no need for a new election to decide the new prime minister as the Conservatives still hold the parliamentary majority. In practice, as most people know very little about their MPs and are voting based on the personality and perceived competency of the party leader (and/or identification with the principals of the party), there will be people calling for a new general election. I didn't vote for the Conservatives, and I'd like to see Labour take their place, but now is not the right time to do so. Not only have we got the uncertainty surrounding Brexit, there's also a civil war going on in the Labour party, which is likely to get worse when the report from the Chilcot Inquiry on the Iraq war is released next week. We need stability right now, new UK elections can wait until 2020. Also, the leader of each party is voted for by the members of that party, and anyone can become a member of a party by paying a small membership fee. If you care about who is the leader of a particular party, you do have the choice to have a say in it.