Similar to the fault with the screen wash on the Fiat that Emily used to have. Fiat in their infinite wisdom only sell the pump complete with a washer bottle at over £100. I piddled about replacing the pump with aftermarket stuff I had lying around. In the end, after much faffing, it turned out to be the in-line none return valve to the windscreen, replaced it with just a joining tube .... sorted.....
Before going for pump replacement, look under the bonnet for the pipework to the front jets, trace it to the OS of the wiper and on the end you may find a plastic plug you can remove to blow air through the pipe and see if you get air out of the nozzles and bubbling sound in the bottle, showing the line is clear!