Think it's still yours until the DVLA receive the log book.
When I sold my first car I couldn't find the log book, so when they turned up, I explained, wrote a receipt and signed it to them. They drove off, then next day, had to go to the post office, get new one posted to me etc, fill out there details and send it off.
Reading your post again, just noticed the Insurance and mot problem, Might be worth giving the DVLA a call and explaining, as the post office are very strict and require Docs.