The business model does work but as Silverjet has demonstrated you need substantial funds behind it to get over the start up costs until you can make money on it. Silverjet has a good model, just needs the right long term investment.
BA has the money and very reduced startup costs as the aircraft and a lot of expertise are coming from mainline, plus they have an established brand and corporate clients, who will probably make the bulk of the London City - New York passengers.
I hope Silverjet comes through but my guess is the brand is damaged now and it will take a lot to restore it, and with the rising cost of fuel their fares might have to rise, which could push potential customers to the majors, who are able to reduce fares and take a hit.