The format wasn't great (too much in too short a time), but one assertion was made that the damage caused by 1 'bag for life' was equal to 100+ disposable bags.

This seems to stem from a UK Government comparative study [0] of supermarket bags, which showed that a cotton reusable bag must be reused 131 times to match the lower environmental impact of a conventional plastic shopping bag used just once.

However non-cotton bags had far lower reuse levels, and it isn't clear at a quick glance how they determine environmental impact. They also neglect to account for double-bagging that used to be prevalant, or the larger bag sizes of "bag-for-life" meaning you need fewer bags for your shopping. It looks from that report that typical bags need to be reused 4 or 5 times to be effective. [1] suggests an average of 6 times.

One thing that has changed though with the 5p charge, coupled with things like Blue Planet -- people think about their use. In the past people would have a bag when buying 2 or 3 things, now they often don't, using pockets or existing bags. The change in attitude is probably more of an impact than bag reuse.

[0] https://assets.publishing.service.gov.uk/government/uploads/... [1] https://www.bbc.co.uk/news/science-environment-36917174