If you look at the legislation, it quite clearly says that the Consumer Rights Act, to which the OP referred, does NOT apply to private sales. Therefore, the arguments about who is responsible for the goods is somewhat fatuous.
In reality, the only comeback you have with private sellers is that they must describe the item properly and not misrepresent them. If an item is misrepresented, then you are entitled to ask for your money back. However, this could be difficult to enforce and your only course of action is the Small Claims Court. So it's still buyer beware!
In terms of items being damaged or lost in transit, then your recourse is with the carrier and obviously the seller would be the person with proof of postage /collection and the onus would be with them to pursue any claim
Hope that helps. Best wishes,Mark