Mould.. tiles.. grout

[NotMyselfWithoutCoffee]

Where am I going wrong.
We moved into a new house a couple of months ago, this bathroom is fully tile apart from the ceiling.
Every time we have a shower the tile wall gets soaked, hence the mouldy grout mainly in the shower area.
The house is an older house approx 30 to 40 years old, mostly solid walls rather than partitioned.
We leave the window open most of the time but it's freezing in there. The condensation takes a few hours to evaporate (we also get condensation on windows so the house is flipping freezing as windows are open to clear the condensation).
The mould is aggressive and I'm having to spray mould and mildew remover every week although it doesn't completely clear it.. Leaves a black stain.
I don't seem to have this issue in the rest of the house apart from mould behind one of the radiators (it's on an external wall in one of the bedrooms but we are going to look into that).
Also in our new build we had trickle vents that were open all the time but I don't recall ever having the same issue with mold.. It still grew but a lot slower and more once a month.

Do you have an extractor fan? If not you need one. Trickle vents would also help.

I would like trickle vents but it might be more expensive.
We don't have an extractor fan but the plan is to eventually get one. I'm not sure how much they cost to install though.
I know we could warm the bathroom more by keeping the heating on for longer but it would cost way more money down the line I think with the way monthly rates are going..there is no radiator in the bathroom but a heated towel rail.
I'm not sure if the tile walls being cold has anything to do with it as well. Our new build had a radioator and the bathroom was a lot smaller so it was warm.

Cold walls give a cold surface for the moisture to condense on. Extractor fan should make a difference but you want to leave it on for some time after showers.

Get yourself a Karcher window Vac and a bunch of old towels. Every time I have a shower I karcher my tiles/shower screen down then give it a dry with an old towel.

Moved into my house 2.5 years ago - tackled the black mould that was there with Cillit Bang mould spray immediately. Been using the vac/drying method ever since and it hasn't come back. I also don't have en extractor fan/trickle vents but only an old sash in my bathroom so that's open a small amount while showering then thrown open for at least 15 minutes post shower no matter the weather. I have zero mould on walls/ceiling.

Second drying the tiles after every use. I do have an extractor fan . My bathroom is not fully tiled. Open the window as well.

If you can't afford a Karcher, just get a cheap squeegee from the pound shop and make sure to squeegee down the tiles every time, then most of the water will go down the plughole. Then dry with towel too.

We've just recently bought a dehumidifier for laundry in another room but is also helping our bathroom dry quicker during the day. My partner gets water all over the bathroom when he showers. We also have an old house with huge amounts of tiling and it's just the shower area that's a bit grim once it's built up over a few weeks.

I try to use the HG grout cleaner, scrubbed in with an old tooth brush and leave bleach soaked cotton pads on any black silicone sealant over night every couple of months - both work really well but I often can't be bothered.

I almost bought at karcher window vac for our bathroom tiles, shower screen and upstairs windows to get the moisture away daily - maybe one of these would be useful?

Hi guys thank you all for the great advice.
I think for the time being I will suck it up and use a towel to dry the tile after we are both done in the shower, although I think long term we will def get a extractor fan.

I will look into a karcher as well but the squeegee is also a fab idea so will make sure I grab one next time I'm doing an order...not sure why I didn't think of that.