To add just a little to Bingley's post. Airing cupboards are for only the last bit of drying or for keeping a set of sheets ready for the guest bed. They are usually heated by the hot water tank (now usually insulated so not a lot of heat escapes) and some hot water pipes. Mine is also heated by the flue from the central heating boiler passing through. The clean washing is dried on the line, or in the tumble-dryer, or on the radiators, or as a last resort by ironing the wretched things. With the English weather, and the older English building practices, the houses are damp from drying the washing in, so you have to have somewhere to keep the important stuff so it doesn't get damp again!
Of course the cupboard gets full of fermenting wine, hyacinths before Christmas, and all the clothes that you don't have wardrobe or drawer space for.
Having just got our daughter to empty "her" wardrobe of most of her clothes, and using it as our seasonal wardrobe, we now hear she is probably off to Frankfurt for 2 years with her boyfriend, and can she store some stuff back in her room please. My wife says fine, but none of it fits me, or what does fit doesn't really do much for me!

Rod