I have travelled quite a lot on both cheap and expensive flights and have never witnessed or heard about theft on the flights, even the cheapest of low-cost flights, although that doesn't mean it doesn't happen.
I have, however, sometimes wondered the same thing when travelling long-haul to notorious destinations like Mexico/Colombia. Things I have considered in order to make my travel more secure are mainly around keeping what I care about close to me (eg. phones, tablets, laptops), either on my person (pockets) or beneath the seat in front of me.
I wouldn't consider a BA flight to America a risky flight. You'll be able to gauge the character of the people sitting around you pretty quickly and you'll more than likely be reassured that they would be as alarmed as you of someone rummaging around an overhead bin that didn't contain their luggage.
Ultimately though, there's always going to be a small risk, and if you can't afford to replace something you either have to keep it close or not take it at all.
A note about checked-in luggage. I never put a lock on my suitcases, since the TSA or equivalent can cut locks off or cut into bags if necessary, and a thief can easily get into a bag. I do put valuable items into my suitcase but never anything too significant (expensive/heavy chargers rather than an SLR/laptop). This is party because of the risk of baggage or item loss, but mostly because of the risk of damage from careless baggage handling.