Place the potatoes in a large saucepan of salted boiling water and cook until al dente. Drain then set aside and allow to cool.
Heat the sunflower oil in a non-stick frying pan and fry the bacon until crispy. Remove the bacon on to some kitchen roll and allow to cool before breaking up into smaller pieces. Reserve any cooking liquids left in the pan.
In a large mixing bowl, mix together the mayonnaise, mustard and vinegar. Add the reserved bacon cooking liquids and whisk well. Fold in the cream then add the chives, potatoes and half of the crispy bacon, stir well to combine.
Place the potato salad in a serving dish and sprinkle on the remaining crispy bacon.
This salad can be served either still warm or cold. If making ahead of time, cover the dish with clingfilm and place in a refrigerator.
For a vegetarian version of this salad simply leave out the bacon.