On the manual P38's there is a button on the central switch panel with a large Cog and a Small Cog on it....this is the Range Selection button...
Into Neutral, press this button - wait for the message on the dash to indicate Low Range has been selected...then into a Drive gear and off you tootle...
Never heard of an 'L' button on the dash before...maybe a photo wouldn't go amiss...!!
EDIT: just looked at the manual...the button with the Cogs has got an 'L' in it!
So if yours does nothing and it is not connected to anything behind it....take the central panel off and look to see if it has fallen below....some times the Transfer Box ECU goes pop and previous owners may disconnect the switch to prevent it being used!!