The One Day Like This hitmakers were invited onto the prestigious late-night programme in 2009 and were hoping it would lead to a breakthrough in the States.
They spent a day at the show's studio in New York rehearsing for their big moment, but when the cameras rolled, they missed out because of timing issues and were "unceremoniously" escorted out of the building.
Frontman Guy Garvey tells Q magazine: "We were livid. No apologies. Nothing. We were unceremoniously ushered out of the studio."