Firstly, be careful with your terminology - it's the chloride ion, Cl<sup>-</sup>, not chlorine, which implies the substance Cl<sub>2</sub>.
Secondly, if there are anioins present, then there must be cations to balance the charge. There could be a number present that are below the detection levels of the techniques that you are using. Alternately, there could be cations present that you are not testing for - like the sodim ion, Na<sup>+</sup>. With tap water, you could look at what Sydney Water adds to tap water, and what it removes, to give you some more evidence to discuss. Certainly, there should be fluoride present.
Did you test the pH? That would give you evidence of levels of hydroxide / hydronium. I would guess the samples would be slightly acidic, due to dissolved CO<sub>2</sub>, which means you could also discuss the formation of the hydrogencarbonate ion.
A test with sulfide would tell you whether there were detctable heavy metals present, too.
Note that a negative result does not necessarily imply a problem with accuracy or reliability. The test for phosphate (say) may accurately and reliably provide no evidence for the presence of phosphate. This does not mean that there are no anions present, nor does it even mean that there is no phosphate present. It does mean that there is no detectable phosphate present, and thus the amount that is present must be below the detection limit of the technique - this includes the possibility that there is none, but you can only say with any certainty that any amount present is less than can be detected.