Although 'free' diagnosis can sometimes be useful they are ultimately hoping to make mega bucks doing repair work. No such thing as a 'free lunch'.
Problem with places like Halfords is they lack the experience in this type of repair. They fall back on information issued by Honda and included in some on line 'trade only' workshop manuals about how many hours of labour certain jobs should take. And quote prices of genuine Honda spares.
Problem is car manufacturers often quote labour time for the job to be done the 'official' way , not always the easiest or quickest way. Main dealerships are happy to charge customers to completely remove a front bumper just to change a headlight bulb, or completely remove a wheel arch lining to fit a brand new,very expensive, genuine part, which will hopefully solve the problem. Sometimes during this process they might discover there was actually a simple problem such as a dodgy electrical terminal. They may fix this free of charge without revealing to you that they misdiagnosed the problem and the £600 cost of the pump hadnt been necessary !
I've never done the job on a Jazz but I think its possible to access the pump by just partially diconnecting just part of the lining. . This may, or may not, save a lot of time, although sometimes a full dismantling saves awkward fiddling. And replacement can be a good used pump or reputable ,much cheaper, aftermarket one. And this assumes the pump actually needs changing.
There could be an electrical problem or poor connection in its wiring, steering column switch etc . I have cured a pump (on a Corsa,) by simply clearing a clogged filter inside the bottom of the washer bottle . (Try inserting a strong jet of water into the washer bottle to see if you can dislodge crud from the bottom of the tank and filter. Use a garden hose, not a pressure washer. ) If you do stir up muck keep the hose in the bottle and eventually all the dirty water comes out as overflow. It might not work, but its free and worth a try.