Not such a neat idea
The usually admirably sensible Gareth Thomas MP has suggested that Labour should have primary elections - http://www.progressives.org.uk/magazine/default.asp?action=magazine&articleid=1039
Yup. Great. So we can be like the Democrats and have our registered supporters pick a string of candidates who make us feel great and rah-rah-radical, then crash and burn in the main election. Remember all those great Presidential candidates the Democrats picked by primary: George McGovern, Walter Mondale, Michael Dukakis, Al Gore, John Kerry ...
And we would get to have yet another set of elections - a sure fire way to counter political apathy. Not.
And rip ourselves to shreds in front of the watching nation. Oh, I forgot, we're quite capable of doing that without a primary.
If you need a 2 word argument against primaries: Howard Dean. Or did he win the Iowa caucus? (answers on a postcard please to...)