Sensible,
Go to "Yahoo" home page.
Click on "Travel" in the menu.
Enter airports LGW & LAX.
Click on "Show me airlines" - this option will show you the cheapest fares and the dates they are available. Should be able to travel Thursday!
I show seats available on American Airlines (+ others) for $315.00 (+ tax) Round Trip. All these fares are 3 day advance purchase.
Good Luck.