It's worth finding out if the mould is caused by condensation (i.e. warm, humid air hitting a cold surface), or water ingress (i.e. water coming in from outside and making your walls damp). If it's the former, there are things you can do to reduce the humidity in your house, get more air circulating, or deal with the mould as it arises. If it's the latter, you really need to get the landlord to fix the problem that is causing water to get into the walls -- not only is this a potentially serious structural problem with the fabric of the building that could destroy any investment the landlord has if left unchecked, but anything you do as a tenant may be quite ineffective.
If it is just condensation though, there are things you can try. Condensation happens when the humidity is high enough, and the surface cold enough, for the moisture held in the air to be released onto that surface. Cold air holds less moisture than hot air, so even though the weather forecast might say it's 90% humidity outside, if the outside air is only 5 degrees C, it will still hold far less moisture than your indoor air at 20 degrees C. So one strategy is to swap out the relatively moist air inside your house for the relatively dry air outside your house. Obviously that incurs a cost -- it gets colder in your house, and therefore it costs more to heat your home. The other strategy is to extract moisture from the air inside your house. The most effective way is with a dehumidifier, but it also includes wiping down windows, shower cubicles, etc. and getting the moisture down the drain or out of the house.
- (£100s) Run a dehumidifier to keep the humidity levels to <70% at least. The dehumidifier will be expensive to buy, and running it will also be expensive at today's electricity prices. (We have a cheap overnight tariff, so we only run it during the "cheap" hours. Still quite expensive though.) You'll find much cheaper options that involve absorbent gels or pellets that will absorb some moisture, but nowhere near enough to make a difference. I'd avoid these if you are already having mould/condensation problems.
- (£30 - £2) Buy a Window Vac and vacuum all your windows, vacuum your shower cubicle after you use it, that sort of thing. Alternatively, a cheap £2 squeegee is fine, but when you use it make sure the water goes outside or down the drain, rather than sitting in the bottom of the shower/windowsill. I.e. squeegee your shower tray too. May sound obvious but apparently not to my family!
- (£5 ish per bottle) HG Mould Spray is amazing at getting rid of mould caused by condensation. If it's caused by condensation, and you deal with the humidity/condensation afterward, you probably won't have to reapply it until the following year at worst. That's been our experience anyway. (If you don't adequately deal with the condensation then you'll probably have to do this a few times over the winter, which is unpleasant and awkward with kids as you need to keep them away and ventilate the room well.)
- (FREE!) Open the window in your shower/bathroom BEFORE you start your shower/bath, and leave it open the whole time. Close it when it feels like the temperature is slightly below the rest of the house.
- (FREE!) You can also open windows in the kitchen when you're boiling stuff -- all that moisture has to go somewhere, so better that it goes out of the window. And since cooking will naturally involve warming up a room, you don't have to worry as much about the heat loss.
- (FREE!) Open your trickle vents above your windows if you have them. It will get slightly colder, but houses/double glazing is usually designed with trickle vents in mind. It won't magically solve all condensation (probably won't do much tbh) but it will contribute slightly to better ventilation.