FPTP was great when there were no real parties. It might be improved a bit by open primaries but in our multiple party system it's undemocratic.
Perhaps an FPTP chamber and a PR one would be better if there are people really attached to the idea that most of their representatives don't vote with the party the overwhelming majority of the time regardless of the opinion of their constituents, and that most people have no idea who they are voting for as they don't look past the party.
FPTP just doesn't work when there are more than two options.
Another point - there's no need to go with pure list-based PR. What's wrong with STV or, worst case, AV? You're still voting for the candidate, not the party, and the result is more representative of the views of the constituency as a whole?
EDIT: It should be noted that, as I recall, the three main parties elect their own leader by STV. The Mayor of London is elected by STV. People appear capable of writing numbers in boxes in those elections, I'm sure they can manage it in general ones
