Yes you are right, we do have a new Prime Minister. In simple terms our Government is formed of whichever political party gains the most seats in Parliament.There are 650 seats and each "holds" an MP who can affiliated to a party or independent but mostly they are partisan. To form a Government, as well as having the most seats, you must have a majority of seats -326.The Prime Minister is generally the leader of the winning party and if this changes throughout the "lifetime" of the Parliament then he or she will become Prime Minister.We don't directly vote for the Prime Minister though people tend to be influenced by the Leader. Each seat represents a constituency- an area of the country in which "X" amount of people live. These constituencies are designated according to reported populations and can be varied but the general idea is that "X" number of people are represented in Parliament by their local Member.The whole has been subject to a "General Election" every 4 to 5 years or unless there is a vote of no confidence which the Government loses-if that happens they have to call an election. I have simplified it and haven't mentioned the Parliaments of Scotland, Wales and Northern Ireland and have kept it to the Government of the United Kingdom as a whole. Nor have I mentioned the House of Lords- they are unelected and are either appointed or in some cases hereditary.