Re: How about Companies House?
"If GDPR gives me some means of finally removing this information, then I will be very glad, although I do think that some of the GDPR regulation (particularly about correcting all archived and backup copies of data) are effectively unworkable within the statutory retention period of UK financial regulations, amongst others."
I'm probably in the same position as you and I'll start giving some of these sites grief if they don't smarten up.
However if you read up about the deletion it does refer to what's technically possible. You don't have to delete from the backup. However it would be smart to retain the deletion request so if you restore from the backup you can redo the deletion from the restored data. Once you've replaced the backup with a post-deletion one you'd then no longer need to retain the request.