Tories are the Conservative Party - a bit like your American Republicans, only not so right-wing.
Labour Party - a bit like your Democrats, only more right-wing.
Liberals Party -no easy comparison and they are irrelevant anyway.

The "Tommie and Teutie" references are from WWI. English soldiers were called "Tommies" (for which I blame Rudyard Kipling) and German soldiers were called "Teuties".