This white mould spring up all over my windowsill pots

Having been previously successful with growing indoor plants (in another flat with marginally better sunlight and exposure), I thought I would be able to grow things in my new flat as well.

However even the simplest plants such as basil seem quite unhappy on my windowsill especially in the colder months.

There’s a tendency for a layer white mould (see photo) to appear on the soil, and this seems quite harmful for the plant as well as attracts some mould gnats.

Mind you, my other, more mature potted plants are doing fine inside, but anything new I plant doesn’t seem to survive.

My baby lemon tree has all but died and I am feeling quite sad about it all.

I’m wondering whether I should even bother trying or whether I should just resign to the fact nothing will grow on my windowsill?

Thanks in advance for your advice.