Heat the oil in a large pan, then add the canned tomatoes, tomato puree, stock, sugar and seasoning, then bring to a simmer. Let the soup bubble for 10 mins until the tomatoes have broken down a little.
Whizz with a stick blender, adding half the pot of lactose free cream as you go. Taste and adjust the seasoning – add more sugar if you need to. Serve in bowls with 1 tbsp or so of the pesto swirled on top, a little more lactose free cream and scatter with basil leaves.