There are separate pumps for the windscreen and headlights, so unlikely both have failed at once.
Check fuses 1 and 3 in the engine bay (both 30 amp).
If not a fuse probably gunk blocking the outlet to the bottle.
Firstly I would check that both pumps run. They are attached to the washer bottle near the bottom. You can hear them with the bonnet open if you get someone to activate them inside the car. If both work, I would syphon out as much water from the bottle as possible and pour some diluted milton fluid into the bottle and wait for a few hours to see if it clears.
If that doesn't work, it's a case of taking the washer bottle out and checking for blockages.