In reality, very few people understood the setup and people have instead been treating them like the usual disposable plastic bags that just happen to cost a bit extra.
People would generally re-use the so-called "single use" thin, free plastic bags as bin liners and are now instead getting much thicker plastic bags and buying additional (also thicker) bin liners which are certainly single-use.
Is it a net win? I'm not convinced. It's definitely great PR, for everyone involved.
Disclaimer: I used to work for an environmental political party which very much supports this plastic bag tax.
There are definitely negative externalities (whether that's paper bags, or bin liners, or food spoilage, etc!) that are entirely ignored when people in general talk about the benefits of the plastic bag tax. We don't know whether there has been any net benefit because that has not been properly studied.
As an example, the UK government has tied the plastic bag tax to charity donations (but supermarkets were promoting charitable donations before any bag tax...?) and accepts self-reporting of sales by supermarkets (not amount of plastic consumed? and "bags for life" are not reportable!!), which makes it complete non-sense https://www.gov.uk/government/publications/carrier-bag-charg...