Look at who flies to LON from NYC: setting aside AA, airlines who have a hub in NYC or LON. As far as AA is concerned, they benefit from BA's extensive network from LHR for connections, which makes their relatively high frequency on the route sustainable, which, in a virtuous circle, makes them more attractive to premium O&D pax. No *A airline is a comparable position. BD has a hub there, but it is a much smaller airline than BA. Moreover, many of its flights are single cabin, which makes the UA/BD combination much less attractive than AA/BA. So UA would be highly dependent on O&D traffic. For premium traffic, they are unattractive compared to BA/AA because of much lower frequency. They would have to compensate with a quality product. UA's product in premium classes is not especially distinguished (and that is being charitable ) and they also have to compete with the Silverjet and Maxjets of this world for that traffic at the lower end of the market and EOS at the top end. No surprise then that they cannot sustain it.
DL and CO do fly from NYC to LGW, but both of them have hubs in NYC.
I am far from sure that BD would be able to sustain it either if the Open Skies agreement is eventually accepted. If BD and UA got together to offer a reasonable frequency between them on the route, then maybe they might just about pull it off, but based on past experience I have limited confidence on the willingness of UA to co-operate actively with BD, so I will not be holding my breath on this one.