Can I just clarify? are you saying you put a massive wardrobe actually in front of the radiator in your bedroom?
I've lived in old houses, and only once had slugs and damp, for the first ten years we didn't have a tumble dryer, so had to dry on radiators and clothes horses in the house. we didn't have a dehumidifier either.
What worked for us, bathroom window always open, bedroom windows opened a crack all night, kitchen window always open an inch at least, and wide open when cooking(we didn't have an extractor fan) all windows opened once a day for 10-15 mins with internal doors open too.
Heating not on a timer but by temperature, so when no body in during the day heating set at 15° and turned up once home, when going to bed heating again set to 15° again. it actually worked out cheaper to heat the house like this, rather then set times where everything in the house gets cold (furniture, floors, walls) not just the air.
The time we started to notice damp and slugs, we were baffled, until it we found that the washing machine pipe had been leaking and the wall behind the machine and floor boards under the lino were soaking. once fixed and dried out no more problems.
In your shoes, I would get a big humidifier (maybe rent one if cheaper) to get rid of as much moisture as possible now, then buy a smaller one to keep on top of it. Start opening windows regularly, fuck the creepy crawlies they won't be as damaging to your families health as the amount of mold and damp in your flat that you have right now.
if you don't change how you live, the double glazing will only make your problems worse.
if the wardrobe is in front of the radiator then get rid of it! it's the most stupid thing I can think you could do in any house. (if it is the case) you'd have to buy a clothes rail instead. until you have the money and time to rejig your bedroom.
Getting a washer/dryer is a good thing too, as people have said they are better made now, and even if you only use it to dry towels and bedding, it would make a huge difference.