Don't know the band, but they do sound a bit like 'Phoenix' who's album I just bought yesterday - alphabetical. The last song they play is just like the first track on the album, really loungy jazz funk bass mastermix sortastuff. Hez
It's taken a while but i have a mate who has just found the answer.
I asked one of our art directors about that BT Broadband ad. He knows one of the TV producers at the agency which did the ad so he phoned him and found out that the music was specially written and commissioned for the commercial. It is performed by a guy called Toff Taylor who works for Poppy Music.