Not sure where you’re located, but every single hot water tank I’ve ever seen (in the US) has been sealed and fed from the same cold water feed that you’d be filling your pot with. The worst thing you’d likely encounter in the hot water tank is mineral deposits.
Would someone translate this for me? Loft tank? Soupcon? Cockpunch?
Even filling in guesses from the context, I don’t understand. Why would water from the hot tap taste worse than from the cold?
The UK, where we require the finest possible water for our tea. Except that we really stopped giving a toss a long time ago, and now people who can make a decent cup of tea are on the verge of extinction. We even have an Ig Nobel Award-for-Literature-winning British Standard (the equivalent of the US Underwriters Laboratory) on the subject - BS6008. I print this out and pin it up in every kitchenette I pass through, in some vain hope that something will rub off.
US hot water tanks may be a little different, but still thank-you no, if it’s all the same. Strictly speaking most of the hot water reservoirs in UK homes are of the immersion heater type, a big enclosed copper cylinder that usually resides in an airing cupboard in the largest bedroom. However, this immersion heater usually takes its water from a big tank in the attic, which definitely isn’t sealed, but there’s usually a bit of insulation over the top to keep it from freezing in winter and to strain out the chunkier lumps falling from above. This tank supplies the heating system and the bathroom cold taps (all non-potable), while the drinking water source in the kitchen is a direct feed from pressurised water mains.
For CurtC: Loft = attic; soupcon; cockpunch.
Try a taste test with water from the hot tap. If you like, do it double-blind and have someone prepare it for you with some cold tap, bottled and filtered water samples too (or whatever), and place the samples in the fridge for a uniform temperature. It should taste a bit flat, maybe with a hint of limescale and notes of copper. And possibly pigeon.
CurtC asked: “Would someone translate this for me? Loft tank? Soupcon? Cockpunch?”
It pretty much sums up New Year’s Eve at Mr F Magnet’s house*. 
*I speak from first-hand experience. But he’s never fed me any pigeon soup because he’s a vegetarian.
Really? Is this actually common? What supplies the tank in the attic?
In the U.S. hot water heaters are almost universally sealed tanks fed by the same mains as the drinking water taps. The only real possible risk from the hot water tank is minerals.
(And, I know this won’t make you feel any different, but even if there was some biological contamination in a water supply, the absolute best way of dealing with it is, you know, um, boiling the water. A lot of people believe this is part of the reason for tea’s popularity with you Empire-building types)
THANK YOU! 
US hot water tanks may be a little different, but still thank-you no, if it’s all the same.
Hot water tanks in the US are sealed and have the same input water as the cold lines. No dead birds, although you might get some accumulated rust in the hot water tank.