Blending potatoes into the soup gives it a thicker consistency, and a dab of olive oil in the soup gives some viscosity that is lacking without cream.
I like to take about 2 cups out of the soup pot and blend it (I used an immersion blender, but a regular blender would work fine too) until it's nice and creamy, then add back in with the rest of the soup. I make a dairy-free corn chowder this way, and it's spooky how creamy it tastes, from the blended corn and potatoes.