Urban legend laws

I am convinced I'd heard it was so that...

If you had a driving licence but were cycling and had had a few drinks and you were stopped by the police that;
if you were carrying your driving licence the you could be done for Drink Driving
if you were NOT carrying your driving licence the you could NOT be done for Drink Driving

What says lazeeLegalAid ?

EDIT: by "drink driving" I mean stuff that would lose you your driving licence