Well just looking at your trip briefly there are a few reasons why the prices you are getting are that high, anytime you fly out of the UK there is about $200 in new taxes that weren't there a year ago, also the airfare from London to Buenos Aires with a 2 week stopover in the US are not the greatest right now, and going through RDU is also adding cost, but if you are willing to be a little flexible I got it down to $1,430 by making a some adjustments(itinerary copied below) I do realize those aren't the ideal connections on the outbound to the UK, but better ones are available either connecting in GRU or FRA but that puts the ticket up around $1,700. It may be possible to drop it even lower by playing around a little more with it.
Buenos Aires (EZE) to London (LHR) - Thu, May 19
Buenos Aires (EZE) to Houston (IAH) - Thu, May 19
Continental 52 Dep: 9:35PM Arr: 6:15AM 10h 40m Boeing 767 Coach (S)
Layover in IAH Fri, May 20 9h 30m
Houston (IAH) to London (LHR) - Fri, May 20
Continental 34 Dep: 3:45PM Arr: 6:55AM 9h 10m Boeing 777 Coach (S)
Sat, May 21
Brussels (BRU) to Washington (IAD) - Sun, May 29
Continental 6077 Dep: 12:00PM Arr: 2:18PM 8h 18m Boeing 777 Coach (S)
OPERATED BY UNITED
Washington (IAD) to Buenos Aires (EZE) - Thu, Jul 14
Continental 6101 Dep: 10:04PM Arr: 9:40AM 10h 36m Boeing 767 Coach (S)
OPERATED BY UNITED Fri, Jul 15
Cost per passenger (including taxes & fees) $1,430.40
Total cost for 1 passenger $1,430.40