Unless you have a points membership that you use enough to have status, I'd look elsewhere, unless you are booking this as an immediate connecting flight the day you arrive or leave the US.
(If you are looking to gain usable European points: American is part of the OneWorld alliance with BA; Delta's international alliance is SkyTeam, and United Airlines is part of Star Alliance.) Of these large international carriers, usually United has the best prices from LAX to MCO ("MCO" is Orlando International; it has that acronym because it was originally named McCoy Field.)
If you are not looking to stockpile points, then you will probably get a better price/schedule on a US domestic carrier such as Southwest or JetBlue. Southwest does not use the reseller sites such as Expedia or Orbitz, so the only place you will find their flights is on
www.southwest.com. (Southwest has the added advantage of 2 free checked bags per passenger, up to 70 lbs each bag.) Southwest is a low-cost carrier, about the same style of service as EasyJet or FlyBe, though the fee structure differs.)
Also, be aware that like London, greater Los Angeles has several commercial airports. LAX is the international airport, but there are 4 more domestics: ONT (Ontario, CA), BNA (John Wayne airport in Orange County near Irvine), BUR (Burbank), and LGB (Long Beach.) The mix of airlines is different at each one, but you can find flights to MCO from all of them.
When comparing prices, be sure to take into account how far your chosen airport is from where you will be in Southern California, so that ground transport doesn't end up costing you a fortune. (For example, from
Disneyland, BNA is the optimal choice, as it is much closer to there than LAX is.) If you are hiring a car when you arrive at LAX, be sure to check on any extra fees for returning it to a different airport, though most of the time there is no add'l fee if it is one of these 5.
Here is a trick to see every airline but Southwest all in one place: Go to
https://matrix.itasoftware.com, and in your "Departing from" field, plug in "LAX, LGB, BUR, SNA, ONT" (the codes for all 5 of the airports within the greater Los Angeles area.) You cannot book on that site, but if you see a flight you like, copy down the details and go look directly for it on the airline's own website.