Hello FlamingJune,
If it just looked pretty and didn't swamp all the other plants, flowers and other beautiful wild flowers it could stay. However, nothing else has a chance to grow. It can be 15" above ground strangling anything in its vincinity and have a root system just as deep as it is tall above ground. I am all for nature, I am creating a wood, a garden, a wildlife pond, a wild area, and vegetable plot but the creeping buttercup is 'spoiling everything'. Do I just give in and let it take over the whole of my garden??