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.