^. Water itself, free of any/all possible ions and contaminants, is usually regarded as a good insulator (though that is a relative term.) Even the slightest concentration of ions, though, and your water will rapidly become a very good conductor.
The amount of current that can flow will be somewhat proportional (it's been a damned long while for me since I've done much physics) to the number density of charge carriers, and the amount of charge they each carry- and these will be the ions in the water. They're going to be responsible for most of the conductivity available in water at relatively low voltages. Quickly googling-
"The electrical resistivity of water (0.2 Ω·m sea water, 2 to 200 Ω·m drinking water, 180000 Ω·m deionized water at 20°C)" first result.
Further googling gives rough guesses of-
"between 33-37 grams per liter"
"less than 600 mg/L is regarded as good quality drinking water."
for sea/tap water, with tap water thus being roughly 60 times less salty- 60*0.2 ~ 12, which already gets us into the above spec for drinking water (which would likely have much less of other forms of ion, and less variety I would expect... anyway, just to demonstrate that the proportionality does somewhat follow from common sense.) Good quality distilled water can reach megaohm-meters in resistivity, mind you- those are ballparks.
The 240V we get at mains is AC, too- not DC. That could impact the dangers of being shocked- though to my understanding, getting whipped by AC is more dangerous, it could have different effects in terms of current flow in the water (fluctuating current directionality/magnitude.) If you wanted to do it as an experiment, you could use a hall effect current sensor around a small channel of water and measure current w.r.t voltage. You could vary salinity/etc for distilled water to measure effect of solute concentration on resistivity, too. Note that the effects are generally temperature dependent.
I should also add that it'd be best to be cautious if designing an experiment to work with mains. If you get your own rectifier setup for DC, make sure that it's rated for whatever current you aim to use (you can use regulators that self-limit for safety, for example. I blew a rectifier trying to power a fan array before I took the effort of slapping a decent regulator on it.) You can also use resistors in series + use a voltage divider to measure resistivity more safely. If you gun straight for the AC instead of DC-rectification prior... well, I've no experience in doing that so can't offer advice.