If you were to buy the cheapest (non-flexible) business class fare many months in advance, you might well get it for significantly less than a flexible economy fare sold one week before departure.
Also note that airlines price on origin and destination, indirect (connecting) flights typically cost less than direct, so if you want to fly from London to New York, in business class, it's almost certainly going to be cheaper to fly somewhere else and to start your journey (and fare) from there, and fly _via London_ to NYC. Specifically you'd fly first to Dublin (or Oslo, or Budapest, or ...), then turn around and fly DUB/OSL/BUD-LON-NYC-LON-DUB/OSL/BUD.
Airline pricing can be very, very counter-intuitive to the uninitiated.
(Source: have paid for 20+ business class flights in the last 12 months, none of which were what I'd call expensive, as I despite being a miles collector I am fairly price sensitive. Just as happy to fly with Ryanair or Easyjet when value for money is to be found there)