Paper bags can be recycled, but that’s an industrial process which has an environmental impact. Better to encourage people to use reusable bags, rather than single use ones
Exactly. Maybe they've noticed that people have been merrily using paper bags only once, thinking that's OK, especially if they recycle it, and the only way the change behaviour is to charge people. But no, it's reduce, reuse then recycle.
If you reuse your bag, it's 20 pence for multiple uses, so the cost per use is tiny, if you don't bother to reuse your bags, the cost adds up.
Reusing bags only a few times can have a significant impact on the number of bags used, on a population level. If you reuse a bag only once, the number of bags used is halved. If you reuse a bag 10 times, the number of bags goes down by 90%. Over the whole population, this is millions, possibly tens or hundreds of millions of bags per year.