Political parties often take the course of villainy when their power is threatened. Both the Democrats and Republicans will work together to legally exclude third parties at the local and State level, because this is where the serious threat to them lies—not in some buffoon running as a third party presidential candidate, who can only serve as a spoiler.
Therefore, the path that is open to third parties is one of planned subversion, in which they run as members of a political party, then, when elected, openly change their party. This was tried with some success by “Larouche Democrats”, but would have to be done at a large enough scale so that the law could not be easily changed to either remove them from office or bar them from running again.
Labour is not threatened. The Tories have become pusillanimous PC pawns and are now polling below Labour. Labour’s main threat is the Liberal Democrat Party. Sure the BNP may take a few district, but this will be more than outmatched by Conservative defection to the UK Independence Party.