1997 Saxo washers not working - but pump makes a noise?

I posted this under another question before, but I now see that's not how this site works, so I thought I'd better start a new question...

My 97 Saxo's washer pump makes a whirring noise but nothing comes out of the rubber tube, if I disconnect it from the pipe on the underside of the bonnet that feeds the jets.

So, the nozzles may or may not still be blocked, but that's not the main problem.

The rear window washer stopped working the same week I bought it. The front washers were working but not very well. They had to be bodged by the garage to get through the last MOT.

When I fill the washer bottle, it seems to fill really fast, then the level sinks very slowly. I'm not sure if it's leaking or if it's just hard to fill - like it has to work its way through in stages.

Is my pump leaking, or is it likely to be a blockage in the main rubber tube? It's hard to see where that goes.