Which is probably the answer to your question. The small pump is usually loacted at or near the washer fluid container. If you're an astute DIY-er you cn change it out fairly easy and save a lot of money... at least here in the U.S., since the labor to change the small pump item is cheaper than the part istself.
Here's a test you can do... with the engine shut off and the hood ... er... the 'bonnet' opened have a friend engage the wiper/washer switch and listen for operation. If it is making a noise it's possible the small diameter hosing that runs to both washer ejectors could be clogged. If so, the clog, in my experience is right at the opening of the sprayer. You can insert a small diameter wire into that apparatus for a short (maybe 1 to 2 inches) to see if it helps. If that doesn't help and you don't have the expertise to change the pump, the next stop is at the repair shop... take you check book or high limit credit card with you!
BTW... it's best to use automobile window washer fluid rather than water in that system since the fluid (very inexpensive... $1.50 a gallon here) and it has some window cleaning additive as well as alcohol to keep it from freezing...