I think it definitely looks fungal. Name of the game is prevention with that stuff. You can prevent it (possibly) from spreading by using fungicides like milk, neem oil, copper based fungicides. Baking soda helps as well. What ever you choose, it needs to be done cosistently on whatever schedule the product describes. More often if it keeps raining.
You're going to want to remove the leaves that are spotted, and trash them. Don't toss them on the ground, or compost them.
If it gets to the point where the plant is getting overwhelmed, or the stems are affected down to the soil level, you'll want to go ahead and dig them up. Trash the remains, don't compost.
Also, mulching your beds will help with splash up from the dirt. Dirt is the source for many of the fungal infection we see in plants. Straw, or leaves, grass clippings...
I'm not thinking blight, but it is some kind of fungal disease, perhaps septoria. We usually see septoria on tomatoes, but it does affect potatoes and eggplants too.
Clip off the affected leaves and trash them (not in compost pile). Then spray the whole plant, including undersides of the leaves with an antifungal: hydrogen peroxide straight from the bottle (which is a 3% solution), diluted milk, baking soda solution.
And follow lindsay's suggestion about mulching and don't water the leaves, just the soil.