Condensation on windows

This is a really common problem (trying searching in the In My Home forum, as I know from experience there will be lots of posts about it there). It happens when moist air hits cold surfaces such as the glass in your windows, and you're right about it leading to mould.

Try to ventilate your home as much as you can, dry washing outside if possible (or put it in the bathroom and open the window if you don't have a drier or space outside). Cover pots on the stove, open windows after a bath or shower. Also consider getting a dehumidifier.

Condensation happens when relative humidity gets to 100%. If air contains a given amount of water, all else being the same, relative humidity rises as temperature falls and falls as temp rises. So if air containing water hits a cold window, it cools and humidity rises to the point where it dumps water as condensation.

Once you know that you can start to manage humidity (and hence condensation). A dehumidifier removes water from the air so can help. Replacing inside air which has picked up a lot of water from your breath and other activities (bathing, showering, cooking, drying clothes) with outside air that has less water in it can help. Increasing your internal temperature will also help as it lowers relative humidity.

The quickest way to condensation damp is a tightly shut up house whilst someone plays "chicken" with the dates trying not to put their heating on. They'll be creating loads of trapped wet air in a cold house which will consequently be dumping condensation on any cold or cooler surface. Drying clothes on radiators is another big culprit and contrary to popular belief, its not a free solution either as the heating system will need to work harder to convert water in the clothes into steam to get it out of the clothes.

Black mould growing where window pane meets frame.

Many moons ago, before we had double glazing, this was quite a problem for me. After scrubbing and wiping away the mould, I discovered that I could prolong the time before the mould re-grew by dipping a cotton bud in neat bleach and painting along the join. Obviously, you wouldn't try this unless your window frames are painted white.

single-glazed bay windows plus complimentary waterfall here - get one of these. Only thing to remember is if you have smaller panes of glass, make sure you get the one with the 2 different sizes of 'sucky thing' (technical term!)

Several years ago I was given some large sheets of Celotex insulation boards, and cut them to fit the ground floor outside window apertures.
This eliminated the condensation ENTIRELY. Not cheap if you had to buy them but it does work.
It moves the dew point.