I've had run ins with Late Blight before. It's a tough one.
The lifeform that causes the infection is P. Infestans. While it is referred to as a fungus, it is not a fungus. Or a virus. Or a bacteria. It is an Oomycete. Kind of a rogue lifeform in a classification all to itself. It reproduces with spores and has some similar behavior to fungi, which is why it is usually referred to as a fungi. It is indigenous to all soils on the planet. There is no getting away from it. You can burn the infected plants, but it remains in the soil. You can solarize the soil, but it will be a few feet away in soil that was not treated. The spores are produced in the kind of quantity that Carl Sagan can best describe, and they travel in the wind.
Treatment, according to just about every County Extension office is to use a copper based fungicide, and in no small amount, with repeated treatment. The fact is, once the conditions are right, this thing reproduces at such a rate that the most you can do is harvest what you can and move on. Organic control would be to use
compost tea. This has the effect of populating leaves and stems with more traditional fungi and bacteria, leaving less room for P. Infestans. It helps, but just a little. If the conditions are right, it's like trying to stop a freight train with a lasso. Physical control would be removing leaves. The effect here is to gain time for fruit to ripen, allowing harvest.
Even when the fruit or tubers are harvested, they can still be destroyed. Late Blight was the cause of the Irish Potato famine. Even though the tubers had been harvested, they rotted in storage. I've seen this firsthand. The potatoes look fine, have been washed, properly stored, and checked upon every other day. Nonetheless, they turn to mush in a couple of days. Monday has a perfect looking potato, Tuesday it has just the slightest grey/brownish area, Wednesday it is mush. The most accurate image I can offer as to the appearance and consistency of this mush is booger snot. Tomatoes turn grey/brown and shrivel, also in just a few days.
This thing primarily attacks solanacia crops: tomato, potato, and supposedly eggplant and peppers. I've not seen it on eggplant and peppers. They tend to ripen during the heat of summer, which is a less suitable environment for P Infestans. Also, the structure of the plant is more open and airy which is less conducive for growth of the pest.
I hate to bear bad news, but those potatoes in the ground don't have much chance. Once the plant is infected, the spread is so rapid that no part of the plant survives. By the time you see the infection on the plant, it has already spread through the plant. Chances are those spuds are already gone. You can try to dig some up. If you find some, wash them, dry them, consume them immediately. You can store them in a cool dry area, but in all honesty, they will turn to mush in a week.
This thing has killed millions of people. Not directly as it is harmless to humans. Instead, it destroys the crops, with potatoes at the top of the list. It is the calories destroyed that starves the people. In 2009 an infestation destroyed tomatoes and potatoes in 17 US states along the east coast and the northeast. You could not find a tomato or potato at a farmers market in NY that year. I lost 300 tomato plants, 600 potatoes. From detection of the first infected plant to the death of the last plant was less than 2 weeks. I managed to harvest about 200 pounds of potatoes, at least half of them rotted within a week. The blue potaotes, Purple Viking, held out the longest.