Jack,
If I understand the Tory, Labour and Lib Dem processes correctly, each constitency branch of the party chooses its own candidate for General and By-elections through balloting its local members. The national party can propose a candidate but the final say remains with the grassroots.
I assume that the SNP and Palid Cymru and the N. Ireland parties work in the same way.
You may, on the other hand, be referring to the way the party leader is chosen. Again, in the main, each party uses a variation of the same process in which the members of the party get the final say in that choice. I believe that for the Tories, if they have 3 or more candidates for leadership (as was the case for Labout this time), their Mps will vote on which 2 candidates should be included on the final ballot; we've seen how Labour works recently (though whether allowing people to join up until the last minute and still be allowed to vote will continue is, I think, open to discussion). The Lib. Dems use a transferable vote system if they require an election.