I can share a bit of detail around what we plan to do about this.
We are unable to stop all types of payments coming through on a card after we’ve blocked it in our systems. I imagine our final solution (disclaimer: not sure when this will be ready) will involve those charges being diverted to a “fraud” account so you don’t see them and they don’t impact your balance.
In all honesty, I don’t know when we will be able to build the “final” solution - something we should be able to do though is whenever we get a charge on a card that has been marked as lost or stolen we should be able to proactively reach out to the customer to help resolve this rather than wait for you to come to us. Monzo customers would have the added benefit that they are likely to see these charges anyway thanks to the realtime notifications.
Additionally, our cards will prefer to go online - if they do this then we can send a script that blocks the card, preventing it from being used subsequently offline.