In 2006 the minimum age for an MP was cut from 21 to 18, and as the PM has to be an MP first, they would have to be at least 18. But realistically they would be older than that - you have to work your way to the top of the party and become party leader before you can become PM.
In UK, you can become a Prime Minister when you get the majority votes, and to be qualified to be a Prime Minister you must be a MP first, therefore, you must be at least 18. The rules are just similar to a MP.
18 is the age limit same as for voting.
The only other requirements are that you are not in prison or have not been declared bankrupt in the last two years.
To become the PM you mist first become an MP, then after years of working your way through the benches you will be but into cabinet, then if you are successfully voted in as leader of the party you must then win an election and be PM
But to actually become the PM only 18, as a minimum.