You mean this one:
.
This was not on TOTP, but was instead on "TOTP Prime" a spinoff show, shown on the digital channel BBC3, shown on wednesdays I think??? which delved a bit deeper and would show interviews with artists.
They did show a ML performance afterwards but this was
another performance on RTL.
Although ofcourse she did perform in the UK during her whirlwind promotional campaign in February 2002, on the top of my head where she performed on the Saturday show (a saturday morning show aimed at teenagers), as well as T4 (channel 4 weekend show aimed at 16-25 year olds)