There's charging and there's charging
There's a difference between "charging" the customer - aka invoicing, and then "charging" - aka taking payment by card or paypal.
I have long since transferred away all my .co.uk domains from this nefarious shower. There was one .uk domain I couldn't transfer. It was a .ltd.uk and somehow the transfer got messed up. I just let it expire and forgot about it. And recently let a .org.uk expire as well.
One important point - I made a point of cancelling all payment methods on record with them, card, paypal, maybe direct debit (can't remember if that one existed). That was not straightforward though either.
Of course they've been sending mountains of emails about "my" various .uk domains, which I just ignore. And then loads of reminders and warnings from Nominet for the same. All getting ignored.