It's generally not done in US politics with other functional democratic countries either, not just the UK. Doing so is simply really bad statecraft.
The problem with weighing on one side in an election in is that regardless of the result, parties and the masses who support them remember that kind of political attack. In a functioning democracy, today's losing party is likely to be the next election's ruling party. The US is going to have to deal with whichever side wins, and it could be really bad for it the day that's a party who now (quite justifiably) views the US as a political enemy.
Setting your country up as the enemy of half the electorate in a foreign nation is usually not in its long-term interest. The only time that's ever going to be worth the risk is if the spurned party is already a political enemy (for example, the Sandinista party in Nicaragua).
To horribly misquote Machiavelli, foreign political parties should be "either caressed or wiped out; because they will avenge minor injuries, but cannot do so for grave ones." So assuming that invading the country and other heavy-handed interventions are off the table, it's not a good idea for the US to be taking sides in its politics.
To counter-point my own post here, I think Trump is a special case. He has a well-earned reputation for being mercurial in his political affections. I don't think anyone at this point views him as a typical US President, or a typical Republican, or feels that anything he says is necessarily indicative of any long-term US feelings or policy (or even his own long-term feelings or policy). So were Corbyn to end up winning, it probably wouldn't surprise anyone to see Trump immediately saying all kinds of nice things about the guy, and offering all kinds of support.