I haven't heard the ads in London, but whoever thinks that you "can" go plane to taxi at LCY within 20 minutes has obviously never been to the place. As Cyrano says, 2 minutes is more like it (I managed 60 seconds once - you've got to be on Gate 2 to do it). I don't think I have ever taken anything like 20 minutes, even with waiting for bags.
Incidentally, Heathrow is in London as well. London Borough of Hillingdon.