Great idea.
Here is my guess :
Tories : 42%LibDems : 29%Labour : 22%Miscellaneous regionalist (for HI and AK) : 1%Others (USIP, ANP, etc) : 6%Tories do well in all the rural areas, leading by even greater margins than GOP in the West and South. LibDems do reasonably well, though not excessively, in relatively wealthy and libertarian-leaning liberal States. Labour vote is concentrated in big cities, and industrial areas or progressive rural areas such as VT or MN. Equivalents of SNP, Plaid or Sinn Fein exist in remote States like AK or HI, even though their influence is far smaller than in UK due to those States not bein very populated. In the 2010 general elections, and with a context comparable to the british one, tories would probably have performed slightly better than in UK, and would be able to govern alone. In the US, LibDems would be the second biggest party at least since the 80's, even though the Labour would keep some importance. Probably, Labour and LibDems would use to ally in order to form coalition governments when they hav a majority in the Parliament.
If we are assuming that there are about 650 Parliament seats as in UK, and that each State is divided in constituencies, the breakdown could be :
Tories : 350LibDems : 200Labour : 95Miscellaneous regionalist (for HI and AK) : 3Others (USIP, ANP, etc) : 2