This happened to me in the middle of Tesco and 2 wine bottles fell out of the bag. The staff quickly mopped up the mess, apologized, and replaced the bottles (and bag). The bags were supplied by Tesco.
Nowadays you have a choice of bags, 5p or 10p. The 10p bags are normally stronger as they are a "bag for life" (well, actually, it means they'll replace it if it breaks, not that it will last forever). Supermarkets could quite legitimately argue that the customer chose the unsuitable bag because they weren't prepared to pay the extra 5p for the bag for the job.