US with UK parties

[Peter the Lefty]

The Conservatives would have to be much more right-wing in America than they are in Britain.  Otherwise, they'd be rivaled as the main party of the right wing by UKIP (the BNP would probably do well in the South as well).  And frankly, because socialism is so demonized in the US, I actually think the Lib Dems would probably have a shot of being the main center-left party.  Labour would be a significant third or fourth party with its main bases of support among blue-collar/unionized workers, and in poor areas.  NYC would probably be an Labour stronghold, but with the Lib Dems dominating Manhattan in general.  The Torries would dominate Wall Street, Sutton Place, and Carnegie Hill.  Labour would probably also dominate urban California, Chicago, etc.  The Lib Dems would probably take much of the bourgeois-Dems vote, especially in the suburban northeast (Middlesex county, for example, since Labour's tax policies may rub them in the wrong direction).  The Torries, if they were the way they are in the UK, would dominate a lot of the moderate Republican areas where people like Michael Bloomberg, Charlie Christ, and Arnold Schwarzenegger would gain a big following, but they'd be wiped out by UKIP in a lot of the tea-party heavy areas and the BNP among Southern whites.  You might have an SNP/Plaid equivalent in Hawaii, and maybe in Texas too.  The Greens would probably be most popular in hippie-heavy cities like Portland, Oregon, San Francisco, Burlington, VT, and a lot of the college towns.  Labour would probably be popular in those areas too if it were "Old Labour," but it might loose a lot of its strength in these areas to the Greens and/or Lib Dems in a lot of these areas if it became "New Labour" (including the Iraq War, top-up fees, etc.)  Though making it "New Labour" might give it some more votes in a lot of the otherwise-Lib Dem suburbs that vote Democrat regularly in real life. 

[Peter the Lefty]

Well, I'm sure they'd be slightly more Laissez-faire, but crazy right-wingers hate free trade too.  If you look at the Constiturion Party's website, it says free trade is "being used to foster socialism...".  It's hilarious how pathetically stupid these people are.  But the BNP would probably do the same thing.  I'd say the parties would be led by:
Conservatives-Mitt Romney, with someone more moderate like Charlie Christ or Michael Bloomberg as deputy leader to balance out Romney's very right-wing positions within the party.  Would also include people like Mary Landrieu, Harry Reid, Lincoln Chaffee, Evan Bayh, Mark Begich, Mark Warner, and Tim Kaine.  
Labour-Err...Nancy Pelosi, or maybe Elizabeth Warren.  Van Jones would be okay if it weren't New Labour, but with the New Labour "modernizations", Warren might be the most left-wing person who could viably become leader
Lib Dems-Barack Obama, 'cause he's a right-wing sellout just like Clegg, and I guess you could say that in 2008, his ideology seemed to be left-liberal.  Jerry Brown, the Clintons, Al Gore, Dianne Feinstein, and other Dems who aren't blue dogs, but also aren't socialists by any stretch of the imagination.  
USIP-The Tea Party.  Michelle Bachman, Rick Santorum, and Newt Gingrich all come to mind for leader.  I suppose it'd be Bachmann.
ANP-David Duke, though maybe Jan Brewer so they'd have better electoral prospects
Green Party-Jill Stein or Ralph Nadar
Rick Perry would lead the Texan National Party lol.  

[Peter the Lefty]

UK 2010 election held in the US (hypothetically), if there weren't a Texan National Party or Plaid Hawaii or any other seperatist parties:
Conservatives-42%
Liberal Democrats-21%
Labour-16%
USIP-15%
ANP-5%
Others-1%

[Peter the Lefty]

You've got to realise that "New Labour", while left of the Democrats, would still have most of the Democrat's rank-and-file.

Lib Dems would have moderates or maverickish lefties. Conservatives would be the non-nutcase proportion of the Republican party. The nutters would be in the USIP.

What each main leader would be in:

Obama: Labour
Biden: Labour
Clinton: Labour
Reid: interesting...could be any of the Big 3.
Pelosi: Labour
Romney: Conservative
Bohnner: Conservative
McConnell: Conservative or perhaps USIP.

Add some more.

It's difficult to explain just how right-wing a country America is.  Most Conservative Democrats (the right-of-Bill Clinton type) as well as the non-tea party Republicans would comprise the Conservative Party.  The Tea Party would be USIP.  The "New Democrats" who aren't seen as "Conservative Democrats" or as "Progressives" (in the American sense) as well as plenty who actually are seen as "Progressive" would be the Lib Dems.  Labour would be the "Progressive Democrats" who are seen as super left-wing here, and it would probably also include the Democratic Socialists of America, Bernie Sanders, etc.