Stem Rot (Southern Blight)

I'm wondering how to get rid of 'southern Blight' or Stem Rot.

I'm trying to grow some tomato plants in pots, and have noticed that there is a white 'fluff' on the stem of one of them. The bottom leaves have begun turning yellow, and look wilted. (This happened to my chilli plant too, I don't know if it's related?)

What can I do about it, if anything?

I understand that it is caused by damp conditions. (It's rainy season here, so I presume that could be a factor).

Any advice would be appreciated.

Thanks.