I believe the cheapest you could find would be London to New York City's JFK Airport, depending on the season; in summer it might be 400-700 dollars, while in winter you might find a special price or good deal for anywhere between 150 (if you're really lucky) and 400.
It's definitely more expensive than flying to California, but if you're going to be spending six months you're going to need to start at one end and make your way across anyway. I would just advise against seeing New England and the northeast in january, when Boston is cold as hell.
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