Aw shucks, it's nice to be appreciated! Now, if I can still fit my head through the door......

On airing cupboard vs. hot press, the former is what most people in England probably call it, and certainly the name I grew up using. Hot press is the Irish terminology, although it might be used regionally in parts of Britain too.
I think the answer to the "big box of water" has been covered pretty well with the links to the plumbing thread, but scanning quickly through that I notice that I did omit one extra detail.
In some houses you'll actually find
two header tanks in the attic, one large and one much smaller. The larger cistern is the one shown in my diagram which feeds the hot-water system below and -- in many cases -- also feeds all the cold faucets around the house except the kitchen. The smaller cistern is the header tank for the heating system and keeps the water level topped up in the closed circuit which takes heat from the boiler to the radiators and/or hot-water cylinder. The float on the ball-valve in this cistern is generally set so that it is usually only about half full, which allows room for expansion when the water in that closed-loop gets hot.
As for the open cisterns, they do indeed collect all manner of dust, dirt, dead spiders, and so on. I've even seen dead birds in them before. I'm sure that a sample of water from many would keep a biologist busy with his microscope trying to identify every little wiggly thing for weeks!
Covers are available for the newer plastic cisterns, or even a makeshift plywood sheet fixed over would do much to keep the debris out. You need to allow for the expansion pipe though (see the diagram).