So many people getting ragey and rude on this thread.
I think you vote for both. This is why:
On the voting slips (someone posted a screenshot earlier) there's the name but the party is displayed even more prominently right next to the box you tick.
I think a lot of people care about their local MP. So for example, let's pretend I'm usually a Tory voter (!) - I might like the Conservatives but absolutely loathe Priti Patel. I might not want to vote for her as my MP.
However, MPs don't always get a free vote in Parliament - sometimes they're whipped to vote a certain way. If they don't follow the party whip they can (and are) effectively ejected (if it's a three line whip). I was reading something the other day that suggests a very large proportion of votes are whipped to a greater or lesser degree.
So actually, the party is central to the person you vote for. Your local MP might seem like a really great person - but if their party whips them to vote a certain way, that's what they'll do. Going back to my previous example, although I don't like Priti Patel, I might feel forced to vote for her anyway because I don't agree with Labour/Green/Lib Dem policies. The party's policies generally are more influential than the individual's personal views - hence why there's such a focus on the party manifesto in pre-election campaigning.
Suggesting the party is irrelevant to the vote is ridiculous. If that was the case, why would it be necessary for the parties to produce a central manifesto? If it were ONLY about your local candidate and their worthiness, you'd want a local manifesto only.
If there's an issue that's of burning importance to you, when you vote you check for the party's stance on the issue. Because it doesn't matter what your MP thinks about the subject if they're whipped to vote a certain way.
That's why for most people the party takes precedence over the local person - because it's the party's manifesto and views that the local MP will be expected to support and implement. And if those central policies change, the MP will be expected to go along with those changes, regardless of their personal views. That's especially the case for big or important issues where they'll be whipped.
I think although you technically vote for the person, morally it would be better for them to have to stand down if they defect. A by-election feels like a fairer process. But I can't say I especially care too much - it's a fairly rare occurrence and we've got much bigger shitstorms currently going on in our political system.