In my experience, I have ordered three times off of Asos, and all three times my order was extremely late (by up to a month), they have apologised and guaranteed it won't happen again every time but it always does.
The bad reviews are driven by poor ordering processes. If you try to correct an ordering mistake within less than a minute of hitting "pay now," they won't allow it. Accidentally fudged my address, now it's going to a different state.