Is it a common one like this.............
http://www.screwfix.c...r-stop-tap-15mm/15440
If it is, open right up and give it something like WD40. I can't imagine that any type of grease would do any harm.
Slightly unscrew the gland nut (at the bottom of the spindle). That'll free up the movement.
If it's still unworkable, then buy a new stop-tap; turn off the supply in the pavement; unscrew the whole valve out of the tap body, and replace with the new one. You won't need the new body.